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Math Journal 10-14 Solve for x. 1. 1 − 3 + 10 = 6 2. 2 + 8 − 6 = 3 − 6 Solve the inequality for x, make a number line and graph the solution. 3. − 13 ≤ −14 4. 1 − 4 −2>6 Unit 3 Day 6: Solving MultiStep 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. -3 x-3> -9 5 +3 +3 -3 x > -6 · 5 5· 5 -3x > -30 -3 -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 < 24 4x – 8 + x > 2 4x - 8 < 24 +8 +8 5x - 8 > 2 + 8 +8 4x< 32 5x > 10 4 4 x< 8 5 5 x>2 Example 3: Solve the inequality. Check your solutions. 2x – 9x + 17 > -4 4x – 9 + 3x < 5 -7x + 17 > -4 - 17 - 17 7x - 9 < 5 +9 +9 -7x > -21 7x < 14 -7 -7 x<3 7 7 x<2 Example 4: Solve the inequality. 5x + 3(x + 4) > 28 5x+ 3x+ 12> 28 8x+ 12> 28 -12 - 12 8x > 16 8 8 x >2 4x – 3(x – 2) < 21 4x - 3x + 6 < 21 x + 6 < 21 -6 - 6 x < 15 Example 5: Solve the inequality. 4x + 12(x - 3) < 28 2x – 5(x – 9) > 27 4x+ 12x- 36 < 28 2x - 5x + 45> 27 16x- 36 < 28 -3x + 45> 27 +36 +36 - 45 -45 16x < 64 -3x > - 18 16 -3 16 x <4 x<6 -3 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.