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:
$4 - 1 > x + 1 - 1$
$3 > x$ or $x < 3$

Step2: Solve second inequality

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

Step3: Combine the solutions

The compound inequality uses "or", so we include all values that satisfy either inequality. Since all numbers less than 3 are already included in numbers less than or equal to 9, the combined solution is all real numbers.

Answer:

Inequality Notation: $\mathbb{R}$ (or $-\infty < x < \infty$)
Number Line: The entire number line is shaded (from negative infinity to positive infinity, with arrows pointing outward on both ends).