Question

Solve the equation and check your solution.



6+3t=8t−14

Answer 1

To solve the equation \( 6 + 3t = 8t - 14 \), we can follow these steps:

1. **Isolate all terms involving \( t \)** on one side of the equation. Start by subtracting \( 3t \) from both sides:

\[
6 = 8t - 3t - 14
\]

This simplifies to:

\[
6 = 5t - 14
\]

2. **Add 14 to both sides** to isolate the term with \( t \):

\[
6 + 14 = 5t
\]

This simplifies to:

\[
20 = 5t
\]

3. **Divide both sides by 5** to solve for \( t \):

\[
t = \frac{20}{5} = 4
\]

Now we have found that \( t = 4 \).

### Checking the Solution

To verify our solution, we can substitute \( t = 4 \) back into the original equation:

\[
6 + 3(4) = 8(4) - 14
\]

Calculating both sides:

Left side:
\[
6 + 12 = 18
\]

Right side:
\[
32 - 14 = 18
\]

Since both sides are equal (18 = 18), our solution \( t = 4 \) is correct.

Thus, the solution is:

\[
\boxed{4}
\]