Question

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

Answer 1

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

### Step 1: Combine like terms
First, combine the \( x \) terms on the left side of the equation.

\[
5x + x = 6x
\]

So, the equation becomes:

\[
6x + 8 = 32
\]

### Step 2: Subtract 8 from both sides
Next, we will isolate the term with \( x \) by subtracting 8 from both sides of the equation.

\[
6x + 8 - 8 = 32 - 8
\]
\[
6x = 24
\]

### Step 3: Divide both sides by 6
Now, divide both sides by 6 to solve for \( x \).

\[
x = \frac{24}{6}
\]
\[
x = 4
\]

### Step 4: Check the solution
To verify the 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:

\[
20 + 8 + 4 = 32
\]

Combining the numbers:

\[
32 = 32
\]

Since both sides are equal, our solution \( x = 4 \) is verified.

### Final Answer
\[
x = 4
\]