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.
4 > x + 1 or x + 1 ≤ 10
answer attempt 1 out of 2
inequality notation:
number line:

Explanation:

Step1: Solve first inequality

Subtract 1 from both sides:
$4 - 1 \geq x + 1 - 1$
$\implies 3 \geq x$ or $x \leq 3$

Step2: Solve second inequality

Subtract 1 from both sides:
$x + 1 - 1 \leq 10 - 1$
$\implies x \leq 9$

Step3: Combine the solutions

The compound inequality uses "or", so we take the union of the two solution sets. Since all values that satisfy $x \leq 3$ also satisfy $x \leq 9$, the combined solution is the broader set.

Answer:

Inequality Notation: $x \leq 9$

For the number line: Draw a closed circle at 9, and shade all values to the left of 9 (including 9) to represent all real numbers less than or equal to 9.