Question

solve for x and graph the solution on the number line below. -4 ≥ x - 11

Explanation:

Step1: Add 11 to both sides

To isolate \( x \), we add 11 to both sides of the inequality \( -4 \geq x - 11 \). This gives us \( -4 + 11 \geq x - 11 + 11 \).

Step2: Simplify both sides

Simplifying the left side: \( -4 + 11 = 7 \). Simplifying the right side: \( x - 11 + 11 = x \). So the inequality becomes \( 7 \geq x \), or equivalently \( x \leq 7 \).

To graph this on the number line: We draw a closed circle at 7 (because the inequality is "less than or equal to") and shade the line to the left of 7 to represent all numbers less than or equal to 7.

Answer:

The solution for \( x \) is \( x \leq 7 \). For the graph, there is a closed circle at 7 and shading to the left of 7 on the number line.