Question

solve for x and graph the solution on the number line below.

$-2x + 1 < -9$ and $-2x + 1 \geq -13$

answer attempt 1 out of 3

$<$ $>$ $\leq$ $\geq$ or

inequality notation:

number line:
number line image with -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12 marked

Explanation:

Step1: Solve \(-2x + 1 < -9\)

Subtract 1 from both sides: \(-2x + 1 - 1 < -9 - 1\)
Simplify: \(-2x < -10\)
Divide both sides by -2 (reverse inequality): \(x > 5\)

Step2: Solve \(-2x + 1 \geq -13\)

Subtract 1 from both sides: \(-2x + 1 - 1 \geq -13 - 1\)
Simplify: \(-2x \geq -14\)
Divide both sides by -2 (reverse inequality): \(x \leq 7\)

Step3: Combine solutions

The "and" means intersection: \(5 < x \leq 7\)

Answer:

Inequality Notation: \(5 < x \leq 7\)
(For the number line: Plot an open circle at 5, a closed circle at 7, and shade between them.)