Question

partner #2 name: ______ solve each inequality, show all work in the space provided, and circle your answer. then check your answers with those of your partner. if you have each solved the problems correctly, your answers should match (including the inequality symbol). if they do not, work with your partner to find and correct the error. #1 $35 > -5(4 - x)$ #2 $-(x - 26) leq x - 4(1 - 2x)$ #3 $-(4x - 15) geq -9(3 + 2x)$ #4 $21 + x > 2(-2 - 5x) + 6x$ #5 $7(x + 1) - 7x < 1 - 6x$ #6 $-2(x - 20) leq 10 - 10(1 + x)$ #7 $-2(9 + 4x) geq -x + 6 - 4x$ #8 $9x - 1 + 11x < 7(11 + x)$ objective: students will solve multi - step inequalities. activities by jill

Explanation:

#1: Solve \(35 > -5(4 - x)\)

Step1: Divide both sides by -5

Reverse inequality: \( -7 < 4 - x \)

Step2: Subtract 4 from both sides

\( -11 < -x \)

Step3: Multiply by -1

Reverse inequality: \( 11 > x \) or \( x < 11 \)

#2: Solve \(-(x - 26) \leq x - 4(1 - 2x)\)

Step1: Expand both sides

\( -x + 26 \leq x - 4 + 8x \)

Step2: Simplify right side

\( -x + 26 \leq 9x - 4 \)

Step3: Add x to both sides

\( 26 \leq 10x - 4 \)

Step4: Add 4 to both sides

\( 30 \leq 10x \)

Step5: Divide by 10

\( 3 \leq x \) or \( x \geq 3 \)

#3: Solve \(-(4x - 15) \geq -9(3 + 2x)\)

Step1: Expand both sides

\( -4x + 15 \geq -27 - 18x \)

Step2: Add 18x to both sides

\( 14x + 15 \geq -27 \)

Step3: Subtract 15 from both sides

\( 14x \geq -42 \)

Step4: Divide by 14

\( x \geq -3 \)

#4: Solve \(21 + x > 2(-2 - 5x) + 6x\)

Step1: Expand right side

\( 21 + x > -4 - 10x + 6x \)

Step2: Simplify right side

\( 21 + x > -4 - 4x \)

Step3: Add 4x to both sides

\( 21 + 5x > -4 \)

Step4: Subtract 21 from both sides

\( 5x > -25 \)

Step5: Divide by 5

\( x > -5 \)

#5: Solve \(7(x + 1) - 7x < 1 - 6x\)

Step1: Expand left side

\( 7x + 7 - 7x < 1 - 6x \)

Step2: Simplify left side

\( 7 < 1 - 6x \)

Step3: Subtract 1 from both sides

\( 6 < -6x \)

Step4: Divide by -6

Reverse inequality: \( -1 > x \) or \( x < -1 \)

#6: Solve \(-2(x - 20) \leq 10 - 10(1 + x)\)

Step1: Expand both sides

\( -2x + 40 \leq 10 - 10 - 10x \)

Step2: Simplify right side

\( -2x + 40 \leq -10x \)

Step3: Add 10x to both sides

\( 8x + 40 \leq 0 \)

Step4: Subtract 40 from both sides

\( 8x \leq -40 \)

Step5: Divide by 8

\( x \leq -5 \)

#7: Solve \(-2(9 + 4x) \geq -x + 6 - 4x\)

Step1: Expand left side

\( -18 - 8x \geq -5x + 6 \)

Step2: Add 8x to both sides

\( -18 \geq 3x + 6 \)

Step3: Subtract 6 from both sides

\( -24 \geq 3x \)

Step4: Divide by 3

\( -8 \geq x \) or \( x \leq -8 \)

#8: Solve \(9x - 1 + 11x < 7(11 + x)\)

Step1: Simplify left side

\( 20x - 1 < 77 + 7x \)

Step2: Subtract 7x from both sides

\( 13x - 1 < 77 \)

Step3: Add 1 to both sides

\( 13x < 78 \)

Step4: Divide by 13

\( x < 6 \)

Answer:

#1: \(x < 11\)
#2: \(x \geq 3\)
#3: \(x \geq -3\)
#4: \(x > -5\)
#5: \(x < -1\)
#6: \(x \leq -5\)
#7: \(x \leq -8\)
#8: \(x < 6\)