Question

solve for t and graph the solution.
9|t - 4| < 9
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 absolute value term

Divide both sides by 9:
$$\frac{9|t - 4|}{9} < \frac{9}{9}$$
Simplify to get: $|t - 4| < 1$

Step2: Rewrite without absolute value

For $|A| < b$, this means $-b < A < b$:
$$-1 < t - 4 < 1$$

Step3: Solve for t

Add 4 to all parts of the inequality:
$$-1 + 4 < t - 4 + 4 < 1 + 4$$
Simplify to get: $3 < t < 5$

Step4: Graph explanation

The solution is all real numbers between 3 and 5, not including 3 and 5. On the number line, place open circles at $t=3$ and $t=5$, then draw a line segment connecting the two open circles.

Answer:

The solution is $3 < t < 5$. To graph it, mark open circles at 3 and 5 on the number line, then shade the segment between them.