Question

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

### Step 1: Combine like terms

On the left side of the equation, we have \(5x\) and \(x\). We can combine these terms:

\[
5x + x = 6x
\]

So the equation now looks like this:

\[
6x + 8 = 32
\]

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

Next, we need to isolate the term with \(x\) by getting rid of the constant term on the left side. We will subtract 8 from both sides of the equation:

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

This simplifies to:

\[
6x = 24
\]

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

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

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

Calculating that gives:

\[
x = 4
\]

### Step 4: Check the solution

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

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

Substituting \(x = 4\):

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

Calculating the left side:

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

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

### Final Answer

Thus, the solution to the equation is:

\[
\boxed{4}
\]