Question

solve for x and graph the solution on the number line below. -9 ≤ -3x + 6 or -3x + 6 ≤ -18. answer attempt 1 out of 2. inequality notation: blank box. number line: number line with -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12 marked, arrow left and right. click and drag to plot lines. submit answer.

Explanation:

Step1: Solve the first inequality \(-9 \leq -3x + 6\)

Subtract 6 from both sides: \(-9 - 6 \leq -3x + 6 - 6\)
Simplify: \(-15 \leq -3x\)
Divide both sides by -3 (remember to reverse the inequality sign): \(\frac{-15}{-3} \geq \frac{-3x}{-3}\)
Simplify: \(5 \geq x\) or \(x \leq 5\)

Step2: Solve the second inequality \(-3x + 6 \leq -18\)

Subtract 6 from both sides: \(-3x + 6 - 6 \leq -18 - 6\)
Simplify: \(-3x \leq -24\)
Divide both sides by -3 (reverse the inequality sign): \(\frac{-3x}{-3} \geq \frac{-24}{-3}\)
Simplify: \(x \geq 8\)

Step3: Combine the solutions (since it's "or")

The solutions are \(x \leq 5\) or \(x \geq 8\)

Answer:

Inequality Notation: \(x \leq 5\) or \(x \geq 8\)

For the number line: Plot a closed circle at 5 and shade to the left, and plot a closed circle at 8 and shade to the right.