Question

directions
select up to 2 number line button(s) below. click to activate and drag the circles on the number line to graph the answer.
graph the solution to the inequality 3|7 - 2x|+ 5 > 8.
-5 -4 -3 -2 -1 0 1 2 3 4 5
lear all

Explanation:

Step1: Isolate the absolute - value expression

Subtract 5 from both sides of the inequality $3|7 - 2x|+5>8$.
$3|7 - 2x|>8 - 5$, so $3|7 - 2x|>3$. Then divide both sides by 3, we get $|7 - 2x|>1$.

Step2: Split the absolute - value inequality

We have two cases:
Case 1: $7 - 2x>1$. Subtract 7 from both sides: $-2x>1 - 7$, so $-2x>-6$. Divide both sides by - 2 and reverse the inequality sign, we get $x < 3$.
Case 2: $7 - 2x<-1$. Subtract 7 from both sides: $-2x<-1 - 7$, so $-2x<-8$. Divide both sides by - 2 and reverse the inequality sign, we get $x>4$.

The solution of the inequality is $x < 3$ or $x>4$. On the number - line, we use an open circle at $x = 3$ and shade to the left, and an open circle at $x = 4$ and shade to the right.

Answer:

The correct number - line button is the one with two open circles and shading in opposite directions (the one with an open circle at 3 and shading to the left and an open circle at 4 and shading to the right, which corresponds to the "O→ O←" option if we assume the options are labeled in a logical way based on the number - line graphing).