Ask a New Question
Menu

How many solutions can be found for the linear equation?





4(x + 5)/2 - 5 = (4x + 1)/1

1 answer

To solve the equation:

\[ \frac{4(x + 5)}{2} - 5 = \frac{4x + 1}{1} \]

let's simplify each side step by step:

  1. Simplify the left side:

    \[ \frac{4(x + 5)}{2} = 2(x + 5) = 2x + 10 \]

    Therefore, the left side becomes:

    \[ 2x + 10 - 5 = 2x + 5 \]

  2. The equation now looks like this:

    \[ 2x + 5 = 4x + 1 \]

  3. Rearranging the equation:

    Subtract \(2x\) from both sides:

    \[ 5 = 4x - 2x + 1 \] \[ 5 = 2x + 1 \]

  4. Subtract 1 from both sides:

    \[ 5 - 1 = 2x \] \[ 4 = 2x \]

  5. Divide by 2:

    \[ x = 2 \]

Conclusion: There is exactly one solution to the equation, which is \( x = 2 \).