Question

solve for x and graph the solution on the number line below.
-2x + 8 > 0 or -12 ≥ -2x + 8
answer attempt 1 out of 2
< > ≤ ≥ or
inequality notation:
number line:
number line from -12 to 12 with tick marks at -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12; arrow left and right
click and drag to plot line.

Explanation:

Step1: Solve \(-2x + 8 > 0\)

Subtract 8 from both sides: \(-2x > -8\)
Divide both sides by -2 (reverse inequality): \(x < 4\)

Step2: Solve \(-12 \geq -2x + 8\)

Subtract 8 from both sides: \(-20 \geq -2x\)
Divide both sides by -2 (reverse inequality): \(10 \leq x\) or \(x \geq 10\)

Step3: Combine solutions (or)

The solutions are \(x < 4\) or \(x \geq 10\)

Answer:

Inequality Notation: \(x < 4\) or \(x \geq 10\)

(For the number line: Plot an open circle at 4 and shade left, plot a closed circle at 10 and shade right.)