Solve for x in the equation 2x + 5 = 11, and provide a step-by-step explanation of the solution process.

1 answer

To solve the equation \( 2x + 5 = 11 \) for \( x \), we will follow these steps:

  1. Isolate the term containing \( x \): We need to get \( 2x \) by itself on one side of the equation. To do this, we can subtract \( 5 \) from both sides of the equation.

    \[ 2x + 5 - 5 = 11 - 5 \]

    Simplifying both sides gives us:

    \[ 2x = 6 \]

  2. Solve for \( x \): Now that we have \( 2x = 6 \), we want to solve for \( x \). To do this, we can divide both sides of the equation by \( 2 \).

    \[ \frac{2x}{2} = \frac{6}{2} \]

    Simplifying this results in:

    \[ x = 3 \]

  3. Check the solution: It's always a good practice to substitute the value of \( x \) back into the original equation to verify our solution.

    Substituting \( x = 3 \) into the original equation \( 2x + 5 \):

    \[ 2(3) + 5 = 6 + 5 = 11 \]

    Since both sides are equal, our solution \( x = 3 \) is confirmed to be correct.

Therefore, the solution to the equation \( 2x + 5 = 11 \) is

\[ \boxed{3} \]