Question

solve for t and graph the solution.
-1 < |t - 39| - 2
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: Isolate the absolute - value expression

Add 2 to both sides of the inequality $-1<|t - 39|-2$.
$-1+2<|t - 39|-2 + 2$, which simplifies to $1<|t - 39|$.

Step2: Rewrite the absolute - value inequality as a compound inequality

The inequality $|a|>b$ ($b>0$) is equivalent to $a>b$ or $a < - b$. So, $1<|t - 39|$ is equivalent to $t-39>1$ or $t - 39<-1$.

Step3: Solve the first inequality $t-39>1$

Add 39 to both sides: $t-39 + 39>1+39$, which gives $t>40$.

Step4: Solve the second inequality $t - 39<-1$

Add 39 to both sides: $t-39 + 39<-1+39$, which gives $t<38$.

Answer:

The solution of the inequality is $t<38$ or $t>40$. On the number - line, we graph an open circle at 38 and an arrow pointing to the left, and an open circle at 40 and an arrow pointing to the right.