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Today’s Lesson Solving Multistep Linear Inequalities Unit 3-Lesson 10 Warm-Up Activity Let’s warm up today by practicing our algebra skills with partners. The sum of 3 and 40 percent of a number is equal to 15. What is the number? Let x = a number 40% = 0.4 3 + 0.4x = 15 to “undo” a positive you must use a negative –3 –3 What you do to one side of 0.4 x = 12 the equation, be sure and do to the other. Let x = a number 3 + 0.4 x = 15 –3 –3 0.4 x = 12 to “undo” multiplication you 0.4 0.4 must divide What you do to one side x = 30 of the equation, be sure and do to the other. The difference of 20 percent of a number and 10 is equal to 90. What is the number? Let x = a number 20% = 0.2 0.2x –10 = 90 to “undo” subtraction you must add +10 +10 What you do to one side 0.2 x = 100 of the equation, be sure and do to the other. Let x = a number 0.2x –10 = 90 +10 +10 0.2 x = 100 to “undo” multiplication you must divide 0.2 0.2 What you do to one side x = 500 of the equation, be sure and do to the other. Leo owns a small thrift shop where the daily revenue averages $650. What can his costs be if he wants a profit of at least $525 per day? Let x = costs 650 – x ≥ 525 –650 –650 to “undo” a positive you must use a negative –x ≥ –125 When you multiply or divide both sides of an inequality by –1 –1 a negative number, the x ≤ 125 direction of the inequality must be changed. The costs must remain below $125. Whole-Class Skills Lesson Today we will be solving multistep linear equations. • When solving one-step inequalities, the steps are the same as the steps for solving one-step equations. • The only important difference is paying added attention to reversing the inequality if you multiply or divide both sides by a negative value. • The same is true for multistep inequalities. Solve for x. –3(2x – 4) + 2x – 5 < –13 –6x + 12 + 2x – 5 < –13 distribute the –3 –4x + 7 < –13 collect like terms subtract 7 from –7 –7 both sides –4x < –20 divide by –4 –4 –4 reverse the x>5 inequality Solve for x. 4 x – 8 < 24 5 +8 +8 add 8 to both sides 5 4 5 multiply by the x < 32 4 5 4 reciprocal x < 40 Solve for x. –3x + 1 ≥ 42 exponent first –3x + 1 ≥ 16 subtract 1 from –1 –1 both sides –3x ≥ 15 –3 –3 divide by –3 reverse the x ≤ –5 inequality Solve for x. 4 + 5x – 6x < 32 exponent first 4 + 5x – 6x < 9 collect like terms 4–x<9 subtract 4 from –4 –4 both sides –x < 5 divide by –1 –1 –1 reverse the x > –5 inequality Solve for x. 3(4x + 5) ≤ 75 distribute the 3 12x + 15 ≤ 75 subtract 15 –15 –15 from both sides 12x ≤ 60 divide by 12 12 12 x≤5