Solve for
t
t
. Give your answer in reduced proper fraction or mixed number.

−
3
t
3
+
3
4
=
−
t
−
6
3
-
3
t
3
+
3
4
=
-t -6
3

t
=
t
=

Let's solve the given equation for \( t \):

The equation is:

\[
- \frac{3t}{3} + \frac{3}{4} = -t - 6
\]

### Step 1: Simplify the terms
Simplify \( - \frac{3t}{3} \):

\[
- \frac{3t}{3} = -t
\]

So the equation becomes:

\[
- t + \frac{3}{4} = -t - 6
\]

### Step 2: Eliminate the \( -t \) terms
Add \( t \) to both sides:

\[
- t + t + \frac{3}{4} = -t + t - 6
\]

This simplifies to:

\[
\frac{3}{4} = -6
\]

### Step 3: Check for any possible contradiction
Clearly, this equation \( \frac{3}{4} = -6 \) is false. There is no value of \( t \) that will satisfy this equation.

### Conclusion:
Since the equation leads to a contradiction, there is **no solution** for \( t \) in this case.

---

Would you like more details or have any questions? Here are 5 related questions for further exploration:

1. What happens when an equation has no solution?
2. How can you identify if an equation has infinite solutions?
3. Can fractions in an equation always lead to no solution?
4. How do you handle equations with variables on both sides?
5. What is the difference between a contradiction and a valid equation?

**Tip**: Always check for contradictions early in the equation-solving process to avoid unnecessary work!

Solve for t. Give your answer in reduced proper fraction or mixed number.
−(3t)/3 + 3/4 = −t − 6

This algebra problem involves solving the linear equation −(3t)/3 + 3/4 = −t − 6. The solution explores simplification of variables and leads to a contradiction, resulting in no solution. Suitable for students in Grades 7-9 studying linear equations and contradictions.

Math Problem Statement

− 3 t 3 + 3 4

− t − 6 3

3 t 3 + 3 4

t

t

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation