Question

solve for ( x ) and graph the solution on the number line below. ( 3x - 5 < -23 ) or ( -14 leq 3x - 5 ) answer attempt 2 out of 4 inequality notation: number line: -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 touch and drag to plot line

Explanation:

Step1: Solve \( 3x - 5 < -23 \)

Add 5 to both sides: \( 3x - 5 + 5 < -23 + 5 \)
Simplify: \( 3x < -18 \)
Divide by 3: \( \frac{3x}{3} < \frac{-18}{3} \)
Result: \( x < -6 \)

Step2: Solve \( -14 \leq 3x - 5 \)

Add 5 to both sides: \( -14 + 5 \leq 3x - 5 + 5 \)
Simplify: \( -9 \leq 3x \)
Divide by 3: \( \frac{-9}{3} \leq \frac{3x}{3} \)
Result: \( -3 \leq x \) (or \( x \geq -3 \))

Step3: Combine solutions with "or"

The solutions are \( x < -6 \) or \( x \geq -3 \)

Answer:

Inequality Notation: \( x < -6 \) or \( x \geq -3 \)

For the number line:

• For \( x < -6 \), draw an open circle at -6 and shade to the left.
• For \( x \geq -3 \), draw a closed circle at -3 and shade to the right.