Question

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

$-x + 6 > 2$ or $-x + 6 \leq -5$

answer attempt 1 out of 3

$< > \leq \geq$ or

inequality notation:

number line:

submit answer

Explanation:

Step1: Solve the first inequality

Solve $-x + 6>2$.
Subtract 6 from both sides: $-x>2 - 6$, so $-x>-4$.
Multiply both sides by - 1 (and reverse the inequality sign): $x < 4$.

Step2: Solve the second inequality

Solve $-x + 6\leq - 5$.
Subtract 6 from both sides: $-x\leq-5 - 6$, so $-x\leq-11$.
Multiply both sides by - 1 (and reverse the inequality sign): $x\geq11$.

Answer:

Inequality Notation: $x < 4$ or $x\geq11$

For the number - line:

• For $x < 4$: There is an open circle at $x = 4$ and an arrow pointing to the left.
• For $x\geq11$: There is a closed circle at $x = 11$ and an arrow pointing to the right.