Question

Solve the following linear equation for x . Then check your answer. Show all your steps for solving and checking. 5x+8+x=32 make it sound like a 7th grader

Answer 1

Sure! Let's solve the equation \(5x + 8 + x = 32\) step by step.

**Step 1: Combine like terms on the left side.**
We see that we have \(5x\) and \(x\) on the left side. We can combine these two terms. Remember that \(x\) is the same as \(1x\), so we can add them together:

\[
5x + x = 6x
\]

Now the equation looks like this:

\[
6x + 8 = 32
\]

**Step 2: Subtract 8 from both sides.**
Next, we want to get \(6x\) by itself, so we'll subtract \(8\) from both sides.

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

This simplifies to:

\[
6x = 24
\]

**Step 3: Divide both sides by 6.**
Now we want to solve for \(x\). Since \(6x\) means \(6\) times \(x\), we divide both sides by \(6\):

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

This simplifies to:

\[
x = 4
\]

**Step 4: Check the solution.**
Now, let's check our answer by plugging \(x = 4\) back into the original equation to see if it works:

Original equation: \(5x + 8 + x = 32\)

Substituting \(x = 4\):

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

Calculating this:

\[
20 + 8 + 4 = 32
\]

Adding those numbers together:

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

So, \(32 = 32\) is true!

**Conclusion:**
The solution to the equation \(5x + 8 + x = 32\) is \(x = 4\), and we checked our answer to confirm that it's correct.