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
inequality notation:
number 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 \(x\geq10\)

Step3: Combine solutions

The solutions are \(x < 4\) or \(x\geq10\), so in inequality notation: \(x < 4\) or \(x\geq10\)

Answer:

Inequality Notation: \(x < 4\) or \(x\geq10\)
(For the number line: - For \(x < 4\), draw an open circle at 4 and shade to the left. - For \(x\geq10\), draw a closed circle at 10 and shade to the right.)