Question

solve for $x$ and graph the solution on the number line below.
$-13 > 2x - 5$ or $2x - 5 \geq 17$
answer attempt 1 out of 2
$<$, $>$, $\leq$, $\geq$, or
inequality notation:
number line:
click and drag to plot line

Explanation:

Step1: Solve first inequality

Start with $-13 > 2x - 5$
Add 5 to both sides:
$-13 + 5 > 2x - 5 + 5$
$-8 > 2x$
Divide by 2:
$\frac{-8}{2} > \frac{2x}{2}$
$x < -4$

Step2: Solve second inequality

Start with $2x - 5 \geq 17$
Add 5 to both sides:
$2x - 5 + 5 \geq 17 + 5$
$2x \geq 22$
Divide by 2:
$\frac{2x}{2} \geq \frac{22}{2}$
$x \geq 11$

Step3: Combine solutions

Combine the two results with "or":
$x < -4$ or $x \geq 11$

Number Line Instructions:

1. For $x < -4$: Draw an open circle at $-4$, then draw an arrow pointing left from the circle to represent all values less than $-4$.
2. For $x \geq 11$: Draw a closed circle at $11$, then draw an arrow pointing right from the circle to represent all values greater than or equal to $11$.

Answer:

$x < -4$ or $x \geq 11$