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

make it shorter

Answer 2

To solve the equation \(5x + 8 + x = 32\), we will start by combining like terms and then isolate \(x\).

### Step 1: Combine like terms
We can combine the \(5x\) and \(x\) on the left side of the equation:

\[
5x + x = 6x
\]

Now the equation looks like this:

\[
6x + 8 = 32
\]

### Step 2: Isolate the variable
Next, we want to isolate \(6x\) by subtracting 8 from both sides:

\[
6x + 8 - 8 = 32 - 8
\]
\[
6x = 24
\]

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

\[
x = \frac{24}{6}
\]
\[
x = 4
\]

### Final Solution
The solution to the equation is:

\[
\boxed{4}
\]

### Step 4: Check the solution
To check our solution, we can substitute \(x = 4\) back into the original equation:

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

Substituting \(x\):

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

Calculating:

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

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

Thus, the value of \(x\) is indeed:

\[
\boxed{4}
\]

Answer 3

Sure! Here's a more concise solution:

### Solve the Equation
1. Start with the original equation:
\[
5x + 8 + x = 32
\]

2. Combine like terms:
\[
6x + 8 = 32
\]

3. Isolate \(6x\) by subtracting 8 from both sides:
\[
6x = 24
\]

4. Solve for \(x\) by dividing by 6:
\[
x = 4
\]

### Check the Solution
Substitute \(x = 4\) back into the original equation:
\[
5(4) + 8 + 4 = 32
\]
Calculating the left side:
\[
20 + 8 + 4 = 32
\]
\[
32 = 32
\]

Since both sides match, the solution is confirmed:

\[
\boxed{4}
\]