Question

solve each problem. show your work$x + 13 > 4$$x - 12 \leq -36$$x - 8 < 10$$x - 52 \geq 54$$x - 10 \leq 14$$x - 8 \geq -97$$x - 23 > 57$$x - 14 < -57$$x - 34 > 38$$x - 13 < 25$$x - 16 \geq -52$$x - 16 \leq 38$$x - 15 < 17$$x - 4 \leq -15$$x - 2 \leq 6$$x - 10 > -103$

Explanation:

Step1: Isolate x, add 13 to both sides

$x + 13 - 13 > 4 - 13$

Step2: Simplify to find x

$x > -9$

Step1: Isolate x, add 12 to both sides

$x - 12 + 12 \leq -36 + 12$

Step2: Simplify to find x

$x \leq -24$

Step1: Isolate x, add 8 to both sides

$x - 8 + 8 < 10 + 8$

Step2: Simplify to find x

$x < 18$

Step1: Isolate x, add 52 to both sides

$x - 52 + 52 \geq 54 + 52$

Step2: Simplify to find x

$x \geq 106$

Step1: Isolate x, add 10 to both sides

$x - 10 + 10 \leq 14 + 10$

Step2: Simplify to find x

$x \leq 24$

Step1: Isolate x, add 8 to both sides

$x - 8 + 8 \geq -97 + 8$

Step2: Simplify to find x

$x \geq -89$

Step1: Isolate x, add 23 to both sides

$x - 23 + 23 > 57 + 23$

Step2: Simplify to find x

$x > 80$

Step1: Isolate x, add 14 to both sides

$x - 14 + 14 < -57 + 14$

Step2: Simplify to find x

$x < -43$

Step1: Isolate x, add 34 to both sides

$x - 34 + 34 > 38 + 34$

Step2: Simplify to find x

$x > 72$

Step1: Isolate x, add 13 to both sides

$x - 13 + 13 < 25 + 13$

Step2: Simplify to find x

$x < 38$

Step1: Isolate x, add 16 to both sides

$x - 16 + 16 \geq -52 + 16$

Step2: Simplify to find x

$x \geq -36$

Step1: Isolate x, add 16 to both sides

$x - 16 + 16 \leq 38 + 16$

Step2: Simplify to find x

$x \leq 54$

Step1: Isolate x, add 15 to both sides

$x - 15 + 15 < 17 + 15$

Step2: Simplify to find x

$x < 32$

Step1: Isolate x, add 4 to both sides

$x - 4 + 4 \leq -15 + 4$

Step2: Simplify to find x

$x \leq -11$

Step1: Isolate x, add 2 to both sides

$x - 2 + 2 \leq 6 + 2$

Step2: Simplify to find x

$x \leq 8$

Step1: Isolate x, add 10 to both sides

$x - 10 + 10 > -103 + 10$

Step2: Simplify to find x

$x > -93$

Answer:

1. $x > -9$
2. $x \leq -24$
3. $x < 18$
4. $x \geq 106$
5. $x \leq 24$
6. $x \geq -89$
7. $x > 80$
8. $x < -43$
9. $x > 72$
10. $x < 38$
11. $x \geq -36$
12. $x \leq 54$
13. $x < 32$
14. $x \leq -11$
15. $x \leq 8$
16. $x > -93$