Question

solve for ( x ) and graph the solution on the number line below.

( -7 leq 2x + 7 leq 31 )

answer attempt 1 out of 3

inequality notation:

number line:

Explanation:

Step1: Subtract 7 from all parts

$$\begin{align*} -7 - 7&\leq 2x+7 - 7\leq 31 - 7\\ -14&\leq 2x\leq 24 \end{align*}$$

Step2: Divide all parts by 2

$$\begin{align*} \frac{-14}{2}&\leq\frac{2x}{2}\leq\frac{24}{2}\\ -7&\leq x\leq 12 \end{align*}$$

Answer:

Inequality Notation: $-7\leq x\leq 12$

To graph on the number line: Place a closed - circle at $x = - 7$ (because the inequality includes equality for $-7$) and at $x = 12$ (because the inequality includes equality for $12$), and then draw a line segment connecting these two points.