Question

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

Answer 1

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

**Step 1: Combine like terms.**
We notice that \(5x\) and \(x\) are like terms, so we can combine them:

\[
5x + x = 6x
\]

Now the equation looks like this:

\[
6x + 8 = 32
\]

**Step 2: Isolate the term with \(x\).**
To isolate the term with \(x\), we need to eliminate the \(8\) on the left side of the equation. We can do this by subtracting \(8\) from both sides:

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

This simplifies to:

\[
6x = 24
\]

**Step 3: Solve for \(x\).**
Now, we divide both sides by \(6\) to solve for \(x\):

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

This simplifies to:

\[
x = 4
\]

**Step 4: Check the solution.**
To ensure that our solution is correct, we can 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:

\[
20 + 8 + 4 = 32
\]

Now, simplifying the left side:

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

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

**Final Answer:**
\[
x = 4
\]