Question

Solve the following linear equation for x . Then check your answer. Show all your steps for solving and checking. 5x+8+x=32 (4 points)

Write the correct answer in paragraph form

Answer 1

To solve the linear equation \(5x + 8 + x = 32\), we will begin by combining like terms.

First, we add the \(5x\) and \(x\) on the left side of the equation:

\[
5x + x = 6x
\]

So, the equation now looks like this:

\[
6x + 8 = 32
\]

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

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

This simplifies to:

\[
6x = 24
\]

To solve for \(x\), we divide both sides of the equation by 6:

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

Thus, we find:

\[
x = 4
\]

Now we will check our solution by substituting \(x = 4\) back into the original equation to ensure both sides are equal. The original equation is:

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

Substituting \(x = 4\):

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

Calculating the left side:

\[
20 + 8 + 4 = 32
\]

Adding these values gives:

\[
32 = 32
\]

Since both sides of the equation are equal, our solution is confirmed. Therefore, the solution to the equation \(5x + 8 + x = 32\) is \(x = 4\).