Question

solve for ( x ) and graph the solution on the number line below. ( 4x - 4 leq 24 ) or ( 4x - 4 geq 44 )
answer attempt 1 out of 2
inequality notation:
number line: number line image

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: \(\frac{4x}{4} \leq \frac{28}{4}\)
Result: \(x \leq 7\)

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

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

Step3: Combine solutions

Since it's "or", combine \(x \leq 7\) and \(x \geq 12\).

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.
• Plot a closed circle at 12 and shade to the right.