Question

Solve the following linear equation for 2. 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’ll follow these steps:

### Step 1: Combine like terms

We can combine \(5x\) and \(x\):

\[
5x + x = 6x
\]

So, the equation becomes:

\[
6x + 8 = 32
\]

### Step 2: Isolate the variable term

Next, we need to isolate the term with \(x\) by subtracting \(8\) from both sides of the equation:

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

Simplifying both sides gives:

\[
6x = 24
\]

### Step 3: Solve for \(x\)

Now, we can solve for \(x\) by dividing both sides of the equation by \(6\):

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

This simplifies to:

\[
x = 4
\]

### Step 4: Check the solution

To ensure our solution is correct, we can substitute \(x = 4\) back into the original equation:

Starting with the original equation:

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

Substituting \(x = 4\):

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

Calculating the left side,

\[
20 + 8 + 4 = 32
\]

Simplifying further,

\[
28 + 4 = 32
\]

Finally,

\[
32 = 32
\]

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

### Conclusion

The solution to the equation \(5x + 8 + x = 32\) is

\[
\boxed{4}
\]