Question

Solve the following linear equation for x Then check
your answer. Show all your steps for solving and
checking.
(4 points)

5x + 8 + x = 32

Answer 1

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

### Step 1: Combine like terms
First, combine \(5x\) and \(x\):
\[
5x + x = 6x
\]
So, the equation becomes:
\[
6x + 8 = 32
\]

### Step 2: Isolate the variable term
Next, subtract 8 from both sides 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 \(x\):
\[
x = \frac{24}{6}
\]
So,
\[
x = 4
\]

### Step 4: Check your answer
To check if \(x = 4\) is correct, substitute \(4\) back into the original equation:
\[
5(4) + 8 + 4 = 32
\]
Calculating the left side:
\[
20 + 8 + 4 = 32
\]
Combining these:
\[
32 = 32
\]

Since both sides of the equation are equal, our solution is confirmed.

### Conclusion
The solution to the equation \(5x + 8 + x = 32\) is:
\[
\boxed{4}
\]