https://file.aiquickdraw.com/mathbot/file/1727063350307hdim15gp.jpg

The inequality in the image is:

\[
3 - 4 \left[ 6 - 7(t + 2) \right] > 4 \left\{ 5 - 2 \left[ 1 - (t + 1) \right] \right\}
\]

Let's solve this step by step.

### Step 1: Simplify both sides

#### Left-hand side:
\[
3 - 4 \left[ 6 - 7(t + 2) \right]
\]
Distribute the \( -7 \) inside the parentheses:
\[
6 - 7(t + 2) = 6 - 7t - 14 = -8 - 7t
\]
Now distribute the \( -4 \):
\[
3 - 4(-8 - 7t) = 3 + 32 + 28t = 35 + 28t
\]

#### Right-hand side:
\[
4 \left\{ 5 - 2 \left[ 1 - (t + 1) \right] \right\}
\]
Simplify inside the brackets:
\[
1 - (t + 1) = 1 - t - 1 = -t
\]
Now distribute the \( -2 \):
\[
5 - 2(-t) = 5 + 2t
\]
Distribute the \( 4 \):
\[
4(5 + 2t) = 20 + 8t
\]

### Step 2: Combine both sides:
We now have the inequality:
\[
35 + 28t > 20 + 8t
\]

### Step 3: Solve for \( t \):
Subtract \( 8t \) from both sides:
\[
35 + 20t > 20
\]
Subtract 35 from both sides:
\[
20t > -15
\]
Now divide by 20:
\[
t > -\frac{15}{20} = -\frac{3}{4}
\]

### Final Answer:
\[
t > -\frac{3}{4}
\]

Would you like a detailed explanation or have any questions about the solution?

Here are some related questions to explore:
1. What are the steps to solve linear inequalities with brackets?
2. How can you check the solution to a linear inequality?
3. What happens if the inequality symbol is reversed during simplification?
4. How do negative numbers affect inequality solutions?
5. Can inequalities have multiple solutions or intervals?

**Tip:** Always check your solution by plugging values back into the original inequality to verify correctness.

Solve the inequality 3 - 4[6 - 7(t + 2)] > 4{5 - 2[1 - (t + 1)]}

Learn how to solve the linear inequality 3 - 4[6 - 7(t + 2)] > 4{5 - 2[1 - (t + 1)]}. This step-by-step solution covers key algebraic concepts such as distributive property and solving linear inequalities, suitable for students in Grades 8-10.

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