Math Journal 10-14. Unit 3 Day 6: Solving Multi- Step Inequalities Essential Question: How do I solve inequalities that require more than two steps?

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Math Journal 10-14

Unit 3 Day 6: Solving Multi- Step Inequalities Essential Question: How do I solve inequalities that require more than two steps?

Process/Steps SIMPLIFY: 1)Apply the distributive property, if necessary 2)Combine like terms on each side Isolate the variable and SOLVE by: 3)Drawing a line under the inequality sign 4)Undo addition or subtraction 5)Undo multiplication or division. If you used a negative number, FLIP THE INEQUALITY SIGN!! ALWAYS: 6)Plug in and check your solution!

Example 1: Solve the inequality. x - 3 > -9 -3 5 + 3 -3 5 x > -6 · 5 5 · -3x > -30 -3 x < 10 To get rid of a fraction: 1) Multiply by the denominator 2) Divide by the numerator OR Multiply by the reciprocal

Example 2: Solve the inequality. Check your solutions. 7x – 3x – 8 2 4x - 8 < 24 + 8 4x < 32 4 4 x < 8 5x- 8 > 2 + 8 5x > 10 5 5 x> 2

Example 3: Solve the inequality. Check your solutions. 2x – 9x + 17 > -4 4x – 9 + 3x < 5 -7x + 17 > -4 - 17 -7x> -21 -7 x < 3 7x - 9 < 5 + 9 7x < 14 7 7 x< 2

Example 4: Solve the inequality. 5x + 3(x + 4) > 28 4x – 3(x – 2) < 21 5x+ 3x + 12> 28 8x+ 12> 28 -12 8x> 16 88 x> 2 4x - 3x + 6< 21 x+ 6< 21 -6 x< 15

Example 5: Solve the inequality. 4x + 12(x - 3) 27 4x+ 12x- 36< 28 16x- 36< 28 +36 16x < 64 2x- 5x+ 45> 27 -3x+ 45> 27 - 45 -3x> - 18 16 x< 4 -3 x< 6

Summary Essential Questions: How do I solve inequalities that require more than two steps? Take 1 minute to write 2 sentences answering the essential questions.

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