Question

solve for t and graph the solution.
8 ≤ 8|t - 16|
click two endpoints to graph a line segment, an endpoint and an arrowhead to graph a ray, or two arrowheads to graph a line. to change endpoints from filled - in circles to empty circles, click on them.

Explanation:

Step1: Divide both sides by 8

Divide the inequality $8\leq8|t - 16|$ by 8. We get $1\leq|t - 16|$.

Step2: Consider two cases

Case 1: $t-16\geq0$ (i.e., $t\geq16$). The inequality becomes $1\leq t - 16$. Add 16 to both sides: $t\geq17$.
Case 2: $t - 16<0$ (i.e., $t<16$). The inequality becomes $1\leq-(t - 16)$. Expand to get $1\leq -t + 16$. Subtract 16 from both sides: $- 15\leq -t$. Multiply both sides by - 1 and reverse the inequality sign: $t\leq15$.

Answer:

The solution is $t\leq15$ or $t\geq17$. On the number - line, click on 15 and an arrowhead to the left for $t\leq15$ (with a filled - in circle at 15) and click on 17 and an arrowhead to the right for $t\geq17$ (with a filled - in circle at 17).