Question

practicevalue or values will replace the variable to make the inequality true.1 match each inequality with the correct solution.i) a $x<-2$i b $x<2$i c $x>-2$i d $x>2$i. $4x + 12 < 20$ii. $55 < 35 + 10x$iii. $-\frac{3}{2}x + 12 > 15$iv. $-8x < 16$2 solve each one-step inequality and graph the solution set on a number line.a $x + 7 ≥ 13$b $-4 > x - 3$c $\frac{x}{4} ≤ \frac{5}{2}$d $18.3 > 6.1x$

Explanation:

Question 1: Match each inequality with the correct solution

Solve each multi-step inequality to find the matching solution:

1. For I. $4x + 12 < 20$:

Subtract 12 from both sides, then divide by 4 to isolate $x$, resulting in $x < 2$.

1. For II. $55 < 35 + 10x$:

Subtract 35 from both sides, then divide by 10 to isolate $x$, resulting in $x > 2$.

1. For III. $-\frac{3}{2}x + 12 > 15$:

Subtract 12 from both sides, multiply by $-\frac{2}{3}$ (reverse inequality sign) to isolate $x$, resulting in $x < -2$.

1. For IV. $-8x < 16$:

Divide both sides by $-8$ (reverse inequality sign) to isolate $x$, resulting in $x > -2$.

Part (a) $x + 7 \geq 13$

Step1: Subtract 7 from both sides

$x + 7 - 7 \geq 13 - 7$

Step2: Simplify to isolate $x$

$x \geq 6$
Graph: Closed circle at 6, arrow pointing right on the number line.

Part (b) $-4 > x - 3$

Step1: Add 3 to both sides

$-4 + 3 > x - 3 + 3$

Step2: Simplify to isolate $x$

$x < -1$
Graph: Open circle at -1, arrow pointing left on the number line.

Part (c) $\frac{x}{4} \leq \frac{5}{2}$

Step1: Multiply both sides by 4

$\frac{x}{4} \times 4 \leq \frac{5}{2} \times 4$

Step2: Simplify to isolate $x$

$x \leq 10$
Graph: Closed circle at 10, arrow pointing left on the number line.

Part (d) $18.3 > 6.1x$

Step1: Divide both sides by 6.1

$\frac{18.3}{6.1} > \frac{6.1x}{6.1}$

Step2: Simplify to isolate $x$

$x < 3$
Graph: Open circle at 3, arrow pointing left on the number line.

Answer:

i. a. $x < -2$ matches III. $-\frac{3}{2}x + 12 > 15$
ii. b. $x < 2$ matches I. $4x + 12 < 20$
iii. c. $x > -2$ matches IV. $-8x < 16$
iv. d. $x > 2$ matches II. $55 < 35 + 10x$

---

Question 2: Solve each one-step inequality and graph the solution set