Question

solving inequalities coloring activity
directions: solve each inequality. circle the color of your answer choice and color the
corresponding areas on the coloring sheet.
1 $-90 \geq 18 x$
2 $\frac{x}{3}>-8$
3 $x - 10 < -26$
4 $19 - x \geq 21$
5 $\frac{x}{3}+7>12$
6 $\frac{-5 + x}{4}>1$
7 $-9(4 + x)>-126$
8 $9(x - 7)<-90$
9 $9 \geq \frac{1 + x}{2}$
10 $-23 < 1 - 4x - 8$
11 $0 \geq 6x - 6x$
12 $15>6x + 1 - 4$
13 $-96 \leq 8(x - 6)$
14 $1 - 4(7 - 6x)<141$
15 $-134 < 8x - 5(1 - 7x)$
16 $-6 + 8(6x + 2)<7x + 10$
17 $-3 + 3x \leq x + 2(x - 4)$
18 $-22 - 4x<-(4 - 5x)$

Explanation:

Step1: Solve inequality \( -90\geq18x \)

Divide both sides by \( 18 \): \( x\leq - 5 \)

Step2: Solve inequality \( \frac{x}{3}>-8 \)

Multiply both sides by \( 3 \): \( x>-24 \)

Step3: Solve inequality \( x - 10<-26 \)

Add \( 10 \) to both sides: \( x<-16 \)

Step4: Solve inequality \( 19 - x\geq21 \)

Subtract \( 19 \) from both sides: \( -x\geq2 \), then multiply by \( - 1 \) (reverse inequality): \( x\leq - 2 \)

Step5: Solve inequality \( \frac{x}{3}+7>12 \)

Subtract \( 7 \) from both sides: \( \frac{x}{3}>5 \), multiply by \( 3 \): \( x > 15 \)

Step6: Solve inequality \( \frac{-5 + x}{4}>1 \)

Multiply both sides by \( 4 \): \( -5+x>4 \), add \( 5 \): \( x>9 \)

Step7: Solve inequality \( -9(4 + x)>-126 \)

Divide both sides by \( -9 \) (reverse inequality): \( 4+x < 14 \), subtract \( 4 \): \( x < 10 \)

Step8: Solve inequality \( 9(x - 7)<-90 \)

Divide both sides by \( 9 \): \( x - 7<-10 \), add \( 7 \): \( x<-3 \)

Step9: Solve inequality \( 9\geq\frac{1 + x}{2} \)

Multiply both sides by \( 2 \): \( 18\geq1 + x \), subtract \( 1 \): \( x\leq17 \)

Step10: Solve inequality \( -23<1 - 4x - 8 \)

Simplify right - hand side: \( -23<-4x - 7 \), add \( 7 \): \( -16<-4x \), divide by \( -4 \) (reverse inequality): \( x < 4 \)

Step11: Solve inequality \( 0\geq6x - 6x \)

Simplify right - hand side: \( 0\geq0 \), which is True for all real numbers

Step12: Solve inequality \( 15>6x + 1 - 4 \)

Simplify right - hand side: \( 15>6x - 3 \), add \( 3 \): \( 18>6x \), divide by \( 6 \): \( x < 3 \)

Step13: Solve inequality \( -96\leq8(x - 6) \)

Divide both sides by \( 8 \): \( -12\leq x - 6 \), add \( 6 \): \( x\geq - 6 \)

Step14: Solve inequality \( 1 - 4(7 - 6x)<141 \)

Expand left - hand side: \( 1-28 + 24x<141 \), simplify: \( 24x-27<141 \), add \( 27 \): \( 24x<168 \), divide by \( 24 \): \( x < 7 \)

Step15: Solve inequality \( -134<8x - 5(1 - 7x) \)

Expand right - hand side: \( -134<8x-5 + 35x \), simplify: \( -134<43x-5 \), add \( 5 \): \( -129<43x \), divide by \( 43 \): \( x>-3 \)

Step16: Solve inequality \( -6 + 8(6x + 2)<7x + 10 \)

Expand left - hand side: \( -6+48x + 16<7x + 10 \), simplify: \( 48x + 10<7x + 10 \), subtract \( 7x \): \( 41x+10 < 10 \), subtract \( 10 \): \( 41x<0 \), divide by \( 41 \): \( x < 0 \)

Step17: Solve inequality \( -3 + 3x\leq x + 2(x - 4) \)

Expand right - hand side: \( -3 + 3x\leq x + 2x-8 \), simplify: \( -3 + 3x\leq3x-8 \), subtract \( 3x \): \( -3\leq - 8 \), which is False (no solution)

Step18: Solve inequality \( -22 - 4x<-(4 - 5x) \)

Expand right - hand side: \( -22 - 4x<-4 + 5x \), add \( 4x \): \( -22<-4 + 9x \), add \( 4 \): \( -18<9x \), divide by \( 9 \): \( x>-2 \)

Answer:

1. \( x\leq - 5 \)
2. \( x>-24 \)
3. \( x<-16 \)
4. \( x\leq - 2 \)
5. \( x > 15 \)
6. \( x>9 \)
7. \( x < 10 \)
8. \( x<-3 \)
9. \( x\leq17 \)
10. \( x < 4 \)
11. All Real Numbers
12. \( x < 3 \)
13. \( x\geq - 6 \)
14. \( x < 7 \)
15. \( x>-3 \)
16. \( x < 0 \)
17. No Solution
18. \( x>-2 \)