Question

solve for x and graph the solution on the number line below. if possible, resolve your answer to a single inequality. in case of no solution (∅), leave the number line blank. -10 > -x - 7 or -x - 7 > -19

Explanation:

Step1: Solve left inequality

Start with $-10 > -x - 7$.
Add 7 to both sides:
$-10 + 7 > -x - 7 + 7$
$-3 > -x$
Multiply by -1 (reverse inequality):
$3 < x$

Step2: Solve right inequality

Start with $-x - 7 > -19$.
Add 7 to both sides:
$-x - 7 + 7 > -19 + 7$
$-x > -12$
Multiply by -1 (reverse inequality):
$x < 12$

Step3: Combine with "or"

Since the original problem uses "or", and the solutions $3 < x$ and $x < 12$ cover all real numbers (every real number is either greater than 3, less than 12, or both), we combine them to represent all real numbers.

Answer:

Inequality Notation: $\mathbb{R}$ (all real numbers)
Number Line: A line with arrows pointing left and right covering the entire number line (no endpoints, as all real numbers are included)