Question

question solve for x and graph the solution on the number line below. 27 ≤ -2x + 7 or 13 > -2x + 7 answer attempt 1 out of 2 inequality notation: number line: number line with -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12

Explanation:

Step1: Solve the first inequality \(27 \leq -2x + 7\)

Subtract 7 from both sides: \(27 - 7 \leq -2x + 7 - 7\)
\(20 \leq -2x\)
Divide both sides by -2 (and reverse the inequality sign): \(\frac{20}{-2} \geq \frac{-2x}{-2}\)
\(-10 \geq x\) or \(x \leq -10\)

Step2: Solve the second inequality \(13 > -2x + 7\)

Subtract 7 from both sides: \(13 - 7 > -2x + 7 - 7\)
\(6 > -2x\)
Divide both sides by -2 (and reverse the inequality sign): \(\frac{6}{-2} < \frac{-2x}{-2}\)
\(-3 < x\) or \(x > -3\)

Step3: Combine the solutions (since it's "or", we take the union)

The solution is \(x \leq -10\) or \(x > -3\)

Answer:

Inequality Notation: \(x \leq -10\) or \(x > -3\)
(For the number line: Plot a closed circle at -10 and shade to the left, and an open circle at -3 and shade to the right.)