Question

solve for $x$ and graph the solution on the number line below. $10leq -x + 7$ or $-x + 7<6$

Explanation:

Step1: Solve the first inequality

Subtract 7 from both sides of $10\leq -x + 7$.
$10-7\leq -x+7 - 7$, which simplifies to $3\leq -x$. Multiply both sides by - 1 and reverse the inequality sign, we get $x\leq - 3$.

Step2: Solve the second inequality

Subtract 7 from both sides of $-x + 7<6$.
$-x+7 - 7<6 - 7$, which simplifies to $-x<-1$. Multiply both sides by - 1 and reverse the inequality sign, we get $x > 1$.

Answer:

The solution is $x\leq - 3$ or $x>1$. On the number - line, we have a closed circle at $x = - 3$ and shade to the left for $x\leq - 3$, and an open circle at $x = 1$ and shade to the right for $x>1$.