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5.3 – Solving Multi-Step Inequalities

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*Just like solving equations*

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*Just like solving equations* Example 1

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*Just like solving equations* Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line.

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*Just like solving equations* Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line. 7x – 5 > 6x – 4

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*Just like solving equations* Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line. 7x – 5 > 6x – 4 -6x -6x

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*Just like solving equations* Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line. 7x – 5 > 6x – 4 -6x -6x x – 5

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*Just like solving equations* Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line. 7x – 5 > 6x – 4 -6x -6x x – 5 > -4

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*Just like solving equations* Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line. 7x – 5 > 6x – 4 -6x -6x x – 5 > -4 +5 +5

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*Just like solving equations* Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line. 7x – 5 > 6x – 4 -6x -6x x – 5 > -4 +5 +5 x

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*Just like solving equations* Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line. 7x – 5 > 6x – 4 -6x -6x x – 5 > -4 +5 +5 x >

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*Just like solving equations* Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line. 7x – 5 > 6x – 4 -6x -6x x – 5 > -4 +5 +5 x > 1

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*Just like solving equations* Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line. 7x – 5 > 6x – 4 -6x -6x x – 5 > -4 +5 +5 x > 1

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*Just like solving equations* Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line. 7x – 5 > 6x – 4 -6x -6x x – 5 > -4 +5 +5 x > 1 0

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*Just like solving equations* Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line. 7x – 5 > 6x – 4 -6x -6x x – 5 > -4 +5 +5 x > 1 0 1

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*Just like solving equations* Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line. 7x – 5 > 6x – 4 -6x -6x x – 5 > -4 +5 +5 x > 1 0 1

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*Just like solving equations* Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line. 7x – 5 > 6x – 4 -6x -6x x – 5 > -4 +5 +5 x > 1 0 1

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Example 2

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Example 2 – Solve –m < -m + 4 and graph. 9

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Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9

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Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9

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Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9

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Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9

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Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m

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Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m <

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Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m < -m + 4

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Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m < -m + 4 +m

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Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m < -m + 4 +m –8m

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Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m < -m + 4 +m –8m <

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Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m < -m + 4 +m –8m < 4

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Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m < -m + 4 +m –8m < 4 -8 -8

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Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m < -m + 4 +m –8m < 4 -8 -8 m

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Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m < -m + 4 +m –8m < 4 -8 -8 m >

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Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m < -m + 4 +m –8m < 4 -8 -8 m >

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Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m < -m + 4 +m –8m < 4 -8 -8 m > -½

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Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m < -m + 4 +m –8m < 4 -8 -8 m > -½

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Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m < -m + 4 +m –8m < 4 -8 -8 m > -½ 0

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Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m < -m + 4 +m –8m < 4 -8 -8 m > -½ 0 -1½-½

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Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m < -m + 4 +m –8m < 4 -8 -8 m > -½ 0 -1½-½

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Example 3

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Example 3 – Define a variable and write an inequality for each problem. Then solve.

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The product of –4 and a number is at least 35.

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Example 3 – Define a variable and write an inequality for each problem. Then solve. The product of –4 and a number is at least 35.

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Example 3 – Define a variable and write an inequality for each problem. Then solve. The product of –4 and a number is at least 35. -4x

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Example 3 – Define a variable and write an inequality for each problem. Then solve. The product of –4 and a number is at least 35. -4x

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Example 3 – Define a variable and write an inequality for each problem. Then solve. The product of –4 and a number is at least 35. -4x >

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Example 3 – Define a variable and write an inequality for each problem. Then solve. The product of –4 and a number is at least 35. -4x >

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Example 3 – Define a variable and write an inequality for each problem. Then solve. The product of –4 and a number is at least 35. -4x > 35

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Example 3 – Define a variable and write an inequality for each problem. Then solve. The product of –4 and a number is at least 35. -4x > 35 -4 -4

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Example 3 – Define a variable and write an inequality for each problem. Then solve. The product of –4 and a number is at least 35. -4x > 35 -4 -4 x <

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Example 3 – Define a variable and write an inequality for each problem. Then solve. The product of –4 and a number is at least 35. -4x > 35 -4 -4 x < -8.75

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?

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75%( )

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%( )

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%( ? )

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%( ? )

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%( ? ) +

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%( ? ) +

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%( ? ) + 25%( )

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%( ? ) + 25%( )

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%( ? ) + 25%( ? )

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%( ? ) + 25%( ? )

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%( ? )

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%( ? )

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x)

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76)

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76) +

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76) + 0.25

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76) + 0.25(x)

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76) + 0.25(x) ≥ 80

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76) + 0.25(x) ≥ 80 57

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76) + 0.25(x) ≥ 80 57 + 0.25x

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76) + 0.25(x) ≥ 80 57 + 0.25x ≥ 80

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76) + 0.25(x) ≥ 80 57 + 0.25x ≥ 80 -57 -57

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76) + 0.25(x) ≥ 80 57 + 0.25x ≥ 80 -57 -57 0.25x

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76) + 0.25(x) ≥ 80 57 + 0.25x ≥ 80 -57 -57 0.25x ≥ 23

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76) + 0.25(x) ≥ 80 57 + 0.25x ≥ 80 -57 -57 0.25x ≥ 23 0.25 0.25

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76) + 0.25(x) ≥ 80 57 + 0.25x ≥ 80 -57 -57 0.25x ≥ 23 0.25 0.25 x

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76) + 0.25(x) ≥ 80 57 + 0.25x ≥ 80 -57 -57 0.25x ≥ 23 0.25 0.25 x ≥

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Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76) + 0.25(x) ≥ 80 57 + 0.25x ≥ 80 -57 -57 0.25x ≥ 23 0.25 0.25 x ≥ 92

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