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

Short answer

Answer 2

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

### Step 1: Combine like terms on the left side.
The equation can be simplified by combining the \( x \) terms:
\[
5x + x = 6x
\]
Thus, the equation becomes:
\[
6x + 8 = 32
\]

### Step 2: Isolate the term with \( x \).
Next, we want to isolate \( 6x \) 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 \( x \):
\[
x = \frac{24}{6}
\]
Thus, we get:
\[
x = 4
\]

### Step 4: Check the solution.
To verify our solution, we will 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 combine:
\[
20 + 8 = 28
\]
And then:
\[
28 + 4 = 32
\]
Since both sides of the equation are equal (\( 32 = 32 \)), our solution is confirmed.

### Final answer:
\[
x = 4
\]

Answer 3

To solve the equation \( 5x + 8 + x = 32 \):

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

2. Isolate \( 6x \):
\[
6x = 32 - 8
\]
\[
6x = 24
\]

3. Divide by 6:
\[
x = \frac{24}{6} = 4
\]

### Check the solution:
Substituting \( x = 4 \) back into the original equation:
\[
5(4) + 8 + 4 = 32
\]
Calculating:
\[
20 + 8 + 4 = 32
\]
\[
32 = 32
\]

The solution is correct.

### Final answer:
\( x = 4 \)