Question

solve for ( x ) and graph the solution on the number line below.

( 4 x - 4 leq 24 ) or ( 4 x - 4 geq 44 )

answer attempt 1 out of 3

inequality notation:

number line:

Explanation:

Step1: Solve the first inequality \(4x - 4\leq24\)

Add \(4\) to both sides: \(4x-4 + 4\leq24 + 4\), so \(4x\leq28\).
Divide both sides by \(4\): \(x\leq\frac{28}{4}\), \(x\leq7\).

Step2: Solve the second inequality \(4x - 4\geq44\)

Add \(4\) to both sides: \(4x-4 + 4\geq44 + 4\), so \(4x\geq48\).
Divide both sides by \(4\): \(x\geq\frac{48}{4}\), \(x\geq12\).

Answer:

Inequality Notation: \(x\leq7\) or \(x\geq12\)

For the number - line:

• For \(x\leq7\): Draw a closed circle at \(7\) (since the inequality includes equality) and shade to the left.
• For \(x\geq12\): Draw a closed circle at \(12\) (since the inequality includes equality) and shade to the right.