 # 5.3 – Solving Multi-Step Inequalities. *Just like solving equations*

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5.3 – Solving Multi-Step Inequalities

*Just like solving equations*

*Just like solving equations* Example 1

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

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

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

*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

*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

*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

*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

*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 >

*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

*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

*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

*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

*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

*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

Example 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 >

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 >

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

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

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

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

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

Example 3

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.

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.

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

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

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 >

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 >

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

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

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 <

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

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%( )

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%( )

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%( ? )

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%( ? )

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%( ? ) +

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%( ? ) +

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%( )

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%( )

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%( ? )

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%( ? )

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%( ? )

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%( ? )

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)

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

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

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

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)

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) +

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

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)

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

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

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

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

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

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

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

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

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

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 ≥

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