Question

Linear Expressions, Equations & Inequalities Unit Test
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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)

Answer 1

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

### Step 1: Combine like terms
Combine the \(x\) terms on the left side:
\[
5x + x = 6x
\]
So the equation becomes:
\[
6x + 8 = 32
\]

### Step 2: Isolate the variable term
Subtract \(8\) from both sides:
\[
6x + 8 - 8 = 32 - 8
\]
This simplifies to:
\[
6x = 24
\]

### Step 3: Solve for \(x\)
Now, divide both sides by \(6\):
\[
x = \frac{24}{6}
\]
Thus, we find:
\[
x = 4
\]

### Step 4: Check the solution
Substitute \(x = 4\) back into the original equation:
\[
5(4) + 8 + 4 = 32
\]
Calculating the left side:
\[
20 + 8 + 4 = 32
\]
This simplifies to:
\[
32 = 32
\]
Since both sides of the equation are equal, the solution is verified.

### Final Answer
The solution to the equation \(5x + 8 + x = 32\) is:
\[
\boxed{4}
\]