Question

solve for t and graph the solution.
$-3 leq \frac{-2t + 1}{3} leq 1$
plot the endpoints. select an endpoint to change it from closed to open. select the middle of a segment, ray, or line to delete it.
-1 0 1 2 3 4 5 6 7 8
submit

Explanation:

Step1: Multiply all parts by 3

$$-3 \times 3 \leq -2t + 1 \leq 1 \times 3$$
$$-9 \leq -2t + 1 \leq 3$$

Step2: Subtract 1 from all parts

$$-9 - 1 \leq -2t \leq 3 - 1$$
$$-10 \leq -2t \leq 2$$

Step3: Divide by -2 (reverse inequalities)

$$\frac{-10}{-2} \geq t \geq \frac{2}{-2}$$
$$5 \geq t \geq -1$$
$$-1 \leq t \leq 5$$

Answer:

The solution is $-1 \leq t \leq 5$. On the number line, plot closed circles at -1 and 5, then draw a segment connecting them.