Question

solve for x and graph the solution on the number line below.
-x + 6 > 2 or -x + 6 ≤ -5
answer
< > ≤ ≥ or
inequality notation:
number line:

Explanation:

Step1: Solve the first inequality

Subtract 6 from both sides of $-x + 6>2$.
$-x+6 - 6>2 - 6$, which simplifies to $-x>-4$. Multiply both sides by - 1 and reverse the inequality sign, we get $x < 4$.

Step2: Solve the second inequality

Subtract 6 from both sides of $-x + 6\leq - 5$.
$-x+6 - 6\leq - 5 - 6$, which simplifies to $-x\leq - 11$. Multiply both sides by - 1 and reverse the inequality sign, we get $x\geq11$.

Answer:

Inequality Notation: $x < 4$ or $x\geq11$
On the number - line: There is an open circle at 4 and the line extends to the left for $x < 4$, and there is a closed circle at 11 and the line extends to the right for $x\geq11$.