**Solve for \[t\].**
*Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.*

\[12t-2 < -5t + 36\]

We are given the inequality:

\[
12t - 2 < -5t + 36
\]

### Step 1: Combine like terms

First, let's add \(5t\) to both sides to move the terms involving \(t\) to the left-hand side:

\[
12t + 5t - 2 < 36
\]

Simplify:

\[
17t - 2 < 36
\]

### Step 2: Isolate the variable

Next, add 2 to both sides to move the constant on the left-hand side:

\[
17t - 2 + 2 < 36 + 2
\]

Simplify:

\[
17t < 38
\]

### Step 3: Solve for \(t\)

Now, divide both sides by 17:

\[
t < \frac{38}{17}
\]

Since \(\frac{38}{17}\) is already in its lowest terms, the solution is:

\[
t < \frac{38}{17}
\]

### Final Answer:
\[
t < \frac{38}{17}
\]

Would you like further clarification or details on this? Here are some related questions you might find helpful:

1. How do you solve inequalities that involve fractions?
2. What happens when you multiply or divide an inequality by a negative number?
3. Can inequalities have multiple solutions? If so, how do you express them?
4. How do you graph the solution of an inequality like this one?
5. What is the difference between strict inequalities and non-strict inequalities?

**Tip**: Always remember to flip the inequality sign when multiplying or dividing by a negative number.

Solve for t. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.

12t - 2 < -5t + 36

Learn how to solve the linear inequality 12t - 2 < -5t + 36 in this step-by-step solution. This problem covers essential algebra concepts such as combining like terms and solving inequalities. Suitable for students in Grades 7-9, with explanations on isolating variables and reducing fractions to lowest terms.

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