Question

StartFraction 4 left parenthesis x plus 1 right parenthesis Over 8 EndFraction equals 3 x minus 2

Answer 1

To solve the equation

\[
\frac{4(x + 1)}{8} = 3x - 2,
\]

let's simplify and solve it step by step.

1. **Simplify the left side**:

\[
\frac{4(x + 1)}{8} = \frac{4}{8}(x + 1) = \frac{1}{2}(x + 1) = \frac{x + 1}{2}.
\]

So the equation becomes:

\[
\frac{x + 1}{2} = 3x - 2.
\]

2. **Eliminate the fraction by multiplying both sides by 2**:

\[
x + 1 = 2(3x - 2).
\]

This simplifies to:

\[
x + 1 = 6x - 4.
\]

3. **Rearranging the equation**:

Subtract \(x\) from both sides:

\[
1 = 5x - 4.
\]

Now, add 4 to both sides:

\[
5 = 5x.
\]

4. **Divide both sides by 5**:

\[
x = 1.
\]

So, the solution to the equation is

\[
\boxed{1}.
\]

5. **Checking the solution**:

Substitute \(x = 1\) back into the original equation:

\[
\frac{4(1 + 1)}{8} = 3(1) - 2.
\]

This simplifies to:

\[
\frac{4 \cdot 2}{8} = 3 - 2.
\]

Further simplification gives:

\[
\frac{8}{8} = 1,
\]

and since \(1 = 1\), the solution \(x = 1\) is indeed correct.