Question

solve for x and graph the solution on the number line below.
5x - 10 ≤ -55 or -35 ≤ 5x - 10
answer attempt 1 out of 3
inequality notation:
number line:

Explanation:

Step1: Solve \( 5x - 10 \leq -55 \)

Add 10 to both sides: \( 5x - 10 + 10 \leq -55 + 10 \)
Simplify: \( 5x \leq -45 \)
Divide by 5: \( x \leq \frac{-45}{5} = -9 \)

Step2: Solve \( -35 \leq 5x - 10 \)

Add 10 to both sides: \( -35 + 10 \leq 5x - 10 + 10 \)
Simplify: \( -25 \leq 5x \)
Divide by 5: \( \frac{-25}{5} \leq x \)
Simplify: \( -5 \leq x \)

Step3: Combine solutions

The compound inequality is \( x \leq -9 \) or \( x \geq -5 \) (note: \( -5 \leq x \) is same as \( x \geq -5 \))

Answer:

Inequality Notation: \( x \leq -9 \) or \( x \geq -5 \)
(For the number line: Plot a closed circle at -9 and shade to the left, and a closed circle at -5 and shade to the right.)