Question

b. test a number for $x$ to determine which region to shade.

c. graph the solution set on the number line.

d. what is the solution set of the inequality?

for problems 3-6, find the solution set of the inequality. begin by solving the related equation to find the boundary number. then graph the solution set on the number line.

1. $3x \leq -18$

1. $\frac{x}{4} \geq 2$

1. $13.6 \leq 5.2 + x$

Explanation:

Problem 3:

Step1: Isolate x by dividing by 3

$\frac{3x}{3} \leq \frac{-18}{3}$

Step2: Simplify to find boundary

$x \leq -6$

Step3: Test point (e.g., x=0)

$3(0) = 0
leq -18$, so shade left of -6.

Step4: Graph: Closed dot at -6, shade left.

Problem 4:

Step1: Isolate x by multiplying by 4

$\frac{x}{4} \times 4 \geq 2 \times 4$

Step2: Simplify to find boundary

$x \geq 8$

Step3: Test point (e.g., x=0)

$\frac{0}{4}=0
geq 2$, so shade right of 8.

Step4: Graph: Closed dot at 8, shade right.

Problem 5:

Step1: Isolate x by subtracting 5.2

$13.6 - 5.2 \leq x$

Step2: Simplify to find boundary

$8.4 \leq x$ or $x \geq 8.4$

Step3: Test point (e.g., x=8)

$13.6
leq 5.2+8=13.2$, so shade right of 8.4.

Step4: Graph: Closed dot at 8.4, shade right.

Answer:

1. Solution set: $x \leq -6$

Graph: Closed dot at -6, shade all values to the left of -6 on the number line.

1. Solution set: $x \geq 8$

Graph: Closed dot at 8, shade all values to the right of 8 on the number line.

1. Solution set: $x \geq 8.4$

Graph: Closed dot at 8.4, shade all values to the right of 8.4 on the number line.