Solve the following linear equation for x . Then check your answer. Show all your steps for solving and checking.5x+8+x=32

1 answer

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

Step 1: Combine like terms

Combine the \( x \) terms on the left side of the equation:

\[ 5x + x = 6x \]

So the equation becomes:

\[ 6x + 8 = 32 \]

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

Subtract 8 from both sides of the equation to isolate the term with \( x \):

\[ 6x + 8 - 8 = 32 - 8 \]

This simplifies to:

\[ 6x = 24 \]

Step 3: Solve for \( x \)

Now, divide both sides by 6 to solve for \( x \):

\[ x = \frac{24}{6} \]

This simplifies to:

\[ x = 4 \]

Step 4: Check the solution

To check the solution, substitute \( x = 4 \) back into the original equation:

The original equation is:

\[ 5x + 8 + x = 32 \]

Substituting in \( x = 4 \):

\[ 5(4) + 8 + 4 = 32 \]

Calculating the left side:

\[ 20 + 8 + 4 = 32 \]

Combine the numbers:

\[ 20 + 8 = 28 \] \[ 28 + 4 = 32 \]

Since both sides of the equation are equal (32 = 32), our solution is confirmed.

Thus, the final answer is:

\[ \boxed{4} \]