Question

Solve the inequality. Graph the solutions.
4 t minus 3less thannegative 15 or 2 t plus 2greater than8
Question content area bottom
Part 1
Solve the inequality. Choose the correct answer below.
A.
tgreater thannegative 2 or tgreater than5
B.
tless thannegative 3 or tless than3
C.
tgreater thannegative 2 or tless than5
D.
tless thannegative 2 or tless than5
E.
tgreater thannegative 3 or tless than3
F.
tless thannegative 2 or tgreater than5
G.
tgreater thannegative 3 or tgreater than3
H.
tless thannegative 3 or tgreater than3

Answer 1

Let's start by solving the inequalities step by step.

**1. Solve \(4t - 3 < -15\)**

\[
4t - 3 < -15
\]

Add 3 to both sides:

\[
4t < -12
\]

Now, divide by 4:

\[
t < -3
\]

**2. Solve \(2t + 2 > 8\)**

\[
2t + 2 > 8
\]

Subtract 2 from both sides:

\[
2t > 6
\]

Now, divide by 2:

\[
t > 3
\]

### Combine the results

Our solutions are:

1. \(t < -3\)
2. \(t > 3\)

Since the original problem was an "or" inequality, the solutions are:

\[
t < -3 \quad \text{or} \quad t > 3
\]

### Final Answer

The correct option that matches our solution is:

**H. \(t < -3\) or \(t > 3\)**

### Graphing the solutions

On a number line, you would show:

- An open circle at -3 and shade to the left for \(t < -3\).
- An open circle at 3 and shade to the right for \(t > 3\).

This visually represents the solution set.