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.