Question

solve the inequality. graph the solution set, and write the solution set in set - builder notation and interval notation. write numbers as simplified fractions or integers.

• 3t - 2 < 1

part: 0 / 3
part 1 of 3
the solution set in set - builder notation is .

Explanation:

Step1: Isolate the term with $t$

Add 2 to both sides.
$$-3t - 2 + 2 < 1 + 2$$
$$-3t < 3$$

Step2: Solve for $t$

Divide by -3, reverse inequality sign.
$$\frac{-3t}{-3} > \frac{3}{-3}$$
$$t > -1$$

Step3: Write set-builder notation

Define the set of all $t$ satisfying $t > -1$.

Answer:

$\{t \mid t > -1\}$

To graph the solution set:

1. Draw a number line.
2. Place an open circle at $-1$ (since $t$ cannot equal $-1$).
3. Shade the portion of the number line to the right of $-1$.

In interval notation, the solution set is $(-1, \infty)$