Question

solve for x and graph the solution on the number line below. -12 < 3x - 6 and -3 ≤ 3x - 6 answer attempt 1 out of 4 < > ≤ ≥ or inequality notation: number line: touch and drag to plot line. submit answer

Explanation:

Step1: Solve the first inequality \( -12 < 3x - 6 \)

Add 6 to both sides: \( -12 + 6 < 3x - 6 + 6 \)
Simplify: \( -6 < 3x \)
Divide both sides by 3: \( \frac{-6}{3} < \frac{3x}{3} \)
Simplify: \( -2 < x \)

Step2: Solve the second inequality \( 3x - 6 \leq -3 \)

Add 6 to both sides: \( 3x - 6 + 6 \leq -3 + 6 \)
Simplify: \( 3x \leq 3 \)
Divide both sides by 3: \( \frac{3x}{3} \leq \frac{3}{3} \)
Simplify: \( x \leq 1 \)

Step3: Combine the two inequalities

From Step1, \( x > -2 \) (note the correction from -2 < x to x > -2 for consistency in notation), and from Step2, \( x \leq 1 \). So the combined inequality is \( -2 < x \leq 1 \)

Answer:

Inequality Notation: \( -2 < x \leq 1 \)
For the number line: Plot an open circle at -2 (since \( x > -2 \), not including -2) and a closed circle at 1 (since \( x \leq 1 \), including 1), then shade the region between -2 and 1.