Question

what does the solution to the inequality $3x - 4 < 5$ look like on a number line?
\bigcirc a. open circle at $\frac{9}{3}$, shading to the left
\bigcirc b. closed circle at $\frac{9}{3}$, shading to the left
\bigcirc c. open circle at $\frac{3}{9}$, shading to the right
\bigcirc d. open circle at 3, shading to the left

when multiplying both sides of $x/4 \leq 8$ by 4, what is the resulting inequality?
\bigcirc a. $x \geq 32$
\bigcirc b. $x \leq 32$
\bigcirc c. $x \geq 2$
\bigcirc d. $x \leq 2$

Explanation:

Step1: Solve $3x - 4 < 5$

Add 4 to both sides: $3x < 9$
Divide by 3: $x < 3$
Open circle at 3, shade left.

Step2: Multiply $x/4 \leq 8$ by 4

$x \leq 32$

Answer:

a. Open circle at $\frac{9}{3}=3$, shading to the left
b. $x \leq 32$