Question

solve for ( x ) and graph the solution on the number line below.
( -36 < -3x - 9 ) or ( -42 geq -3x - 9 )
answer attempt 3 out of 4
inequality notation: ( x < 9 ) or ( x geq 11 )
number line:
(touch and drag to plot line)
submit answer

Explanation:

Step1: Solve the first inequality \(-36 < -3x - 9\)

Add 9 to both sides: \(-36 + 9 < -3x - 9 + 9\)
Simplify: \(-27 < -3x\)
Divide both sides by -3 (and reverse the inequality sign): \(\frac{-27}{-3} > \frac{-3x}{-3}\)
Simplify: \(9 > x\) or \(x < 9\)

Step2: Solve the second inequality \(-42 \geq -3x - 9\)

Add 9 to both sides: \(-42 + 9 \geq -3x - 9 + 9\)
Simplify: \(-33 \geq -3x\)
Divide both sides by -3 (and reverse the inequality sign): \(\frac{-33}{-3} \leq \frac{-3x}{-3}\)
Simplify: \(11 \leq x\) or \(x \geq 11\)

Step3: Combine the solutions

The solutions to the compound inequality are \(x < 9\) or \(x \geq 11\)

Answer:

Inequality Notation: \(x < 9\) or \(x \geq 11\)

For the number line:

• For \(x < 9\), draw an open circle at 9 and shade to the left.
• For \(x \geq 11\), draw a closed circle at 11 and shade to the right.