Question

solve for x and graph the solution on the number line below.
4x - 4 ≤ 24 or 4x - 4 ≥ 44
answer attempt 1 out of 2
inequality notation:
number line:
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
click and drag to plot line.

Explanation:

Step1: Solve \(4x - 4 \leq 24\)

Add 4 to both sides: \(4x - 4 + 4 \leq 24 + 4\)
Simplify: \(4x \leq 28\)
Divide by 4: \(x \leq \frac{28}{4} = 7\)

Step2: Solve \(4x - 4 \geq 44\)

Add 4 to both sides: \(4x - 4 + 4 \geq 44 + 4\)
Simplify: \(4x \geq 48\)
Divide by 4: \(x \geq \frac{48}{4} = 12\)

Step3: Combine solutions

Since it's "or", the solution is \(x \leq 7\) or \(x \geq 12\)

Answer:

Inequality Notation: \(x \leq 7\) or \(x \geq 12\)

For the number line: Plot a closed circle at 7 and shade to the left, and a closed circle at 12 and shade to the right.