Question

solve the inequality. write your answer in inequality notation, then graph the solution.
$5 \leq 2x + 7 < 11$

Explanation:

Step1: Subtract 7 from all parts

$5 - 7 \leq 2x + 7 - 7 < 11 - 7$
$-2 \leq 2x < 4$

Step2: Divide all parts by 2

$\frac{-2}{2} \leq \frac{2x}{2} < \frac{4}{2}$
$-1 \leq x < 2$

Answer:

Inequality notation: $\boldsymbol{-1 \leq x < 2}$

For the graph:

1. Plot a filled (closed) dot at $x=-1$ (to represent the $\leq$ condition, including -1 in the solution).
2. Plot an open dot at $x=2$ (to represent the $<$ condition, excluding 2 from the solution).
3. Draw a solid line segment connecting the two dots, showing all values between -1 and 2 are included.