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Solve the following linear equation for x.

Then check your answer. Show all your steps for solving and checking.
5x+ 8+x=32

3 answers

To solve the linear equation \( 5x + 8 + x = 32 \), we will follow these steps:

Step 1: Combine like terms on the left side.

The equation can be simplified by combining the \( x \) terms: \[ 5x + x = 6x \] Thus, the equation becomes: \[ 6x + 8 = 32 \]

Step 2: Isolate the term with \( x \).

Next, we want to isolate \( 6x \) by subtracting \( 8 \) from both sides: \[ 6x + 8 - 8 = 32 - 8 \] This simplifies to: \[ 6x = 24 \]

Step 3: Solve for \( x \).

Now, we divide both sides by \( 6 \) to solve for \( x \): \[ x = \frac{24}{6} \] Thus, we get: \[ x = 4 \]

Step 4: Check the solution.

To verify our solution, we will substitute \( x = 4 \) back into the original equation. The original equation is: \[ 5x + 8 + x = 32 \] Substituting \( x = 4 \): \[ 5(4) + 8 + 4 = 32 \] Calculating the left side: \[ 20 + 8 + 4 = 32 \] Now combine: \[ 20 + 8 = 28 \] And then: \[ 28 + 4 = 32 \] Since both sides of the equation are equal (\( 32 = 32 \)), our solution is confirmed.

Final answer:

\[ x = 4 \]

Short answer

To solve the equation \( 5x + 8 + x = 32 \):

  1. Combine like terms: \[ 6x + 8 = 32 \]

  2. Isolate \( 6x \): \[ 6x = 32 - 8 \] \[ 6x = 24 \]

  3. Divide by 6: \[ x = \frac{24}{6} = 4 \]

Check the solution:

Substituting \( x = 4 \) back into the original equation: \[ 5(4) + 8 + 4 = 32 \] Calculating: \[ 20 + 8 + 4 = 32 \] \[ 32 = 32 \]

The solution is correct.

Final answer:

\( x = 4 \)