Question

solve for x and graph the solution on the number line below. -x + 3 > 2 or -6 > -x + 3 answer < > ≤ ≥ or inequality notation: number line: -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

Explanation:

Step1: Solve the first inequality

Subtract 3 from both sides of $-x + 3>2$. We get $-x+3 - 3>2 - 3$, which simplifies to $-x>-1$. Multiply both sides by - 1 and reverse the inequality sign, so $x < 1$.

Step2: Solve the second inequality

Subtract 3 from both sides of $-6>-x + 3$. We have $-6-3>-x+3 - 3$, which simplifies to $-9>-x$. Multiply both sides by - 1 and reverse the inequality sign, so $x>9$.

Answer:

Inequality Notation: $x < 1$ or $x>9$
On the number - line, we have an open circle at 1 and shade to the left for $x < 1$, and an open circle at 9 and shade to the right for $x>9$.