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) please

Answer 1

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

### Step 1: Combine like terms
First, combine the \( x \) terms on the left side of the equation:

\[
5x + x = 6x
\]

Thus, the equation simplifies to:

\[
6x + 8 = 32
\]

### Step 2: Isolate the variable term
Next, we want to isolate the term with \( x \). 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 can solve for \( x \) by dividing both sides by 6:

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

This simplifies to:

\[
x = 4
\]

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

Original equation:

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

Substituting \( x = 4 \):

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

Now calculate:

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

Since both sides of the equation are equal, our solution is confirmed to be correct.

### Final Answer
\[
x = 4
\]