Solve for t
 −3t−(5−t)>−9(t−4)+7t
 there are no solutions, enter \text{None}None​. If the solutions are all real numbers, enter \text{All}All​.
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Enter the solution in interval notation. If no solution exists, enter \text{None}None​.

Let's solve the inequality:

\[
-3t - (5 - t) > -9(t - 4) + 7t
\]

### Step 1: Simplify both sides

Distribute on both sides:

\[
-3t - 5 + t > -9(t - 4) + 7t
\]
\[
-3t - 5 + t > -9t + 36 + 7t
\]

Simplify further:

\[
-2t - 5 > -2t + 36
\]

### Step 2: Eliminate like terms

Add \(2t\) to both sides to eliminate the variable on both sides:

\[
-5 > 36
\]

### Step 3: Analyze the inequality

The inequality \(-5 > 36\) is false. This is a contradiction, meaning the original inequality has **no solution**.

### Final Answer:
\[
\text{None}
\]

Let me know if you'd like more details or have any questions!

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Here are some related questions:

1. How do you solve inequalities with variable terms on both sides?
2. What are some common mistakes in solving linear inequalities?
3. How do you graph inequalities on a number line?
4. How do contradictions in inequalities lead to no solution?
5. How can you tell when an inequality has all real numbers as solutions?

**Tip**: Always check for contradictions after simplifying inequalities; they can indicate that no solution exists.

Solve for t: -3t - (5 - t) > -9(t - 4) + 7t. If there are no solutions, enter None. If the solutions are all real numbers, enter All.

Explore how to solve the inequality -3t - (5 - t) > -9(t - 4) + 7t step-by-step. This example demonstrates how contradictions can lead to no solution for inequalities. Key concepts include simplifying expressions and the distributive property. Suitable for students in Grades 9-11.

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