Question

Solving Linear Equations Unit Test 19 of 1919 of 19 Items Question Solve the following linear equation for x . 8th Grade Verbiage. Then check your answer. Show all your steps for solving and checking. 5x+8+x=32 (4 points) Math Short Answer Rubric (4 points) Points Awarded Criteria 4 The answer is clear and correct. The answer shows that the student used problem-solving skills and reasoning. All work is shown or explained. 3 The answer is mostly correct. The student made small errors while solving. The answer shows that the student used some problem-solving skills and reasoning. Most work is shown or explained. 2 The answer is partially correct. The student made errors while solving. The answer shows that the student used some problem-solving skills or reasoning. Some work is shown or explained. 1 The answer is incorrect. The student made errors while solving. The answer shows little problem-solving skills or reasoning. Little or no work is shown. 0 The question is not answered. Skip to navigation

Answer 1

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

### Step 1: Combine Like Terms
First, we can combine the \(5x\) and \(x\) on the left side of the equation.

\[
5x + x = 6x
\]

So the equation becomes:

\[
6x + 8 = 32
\]

### 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 of the equation.

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

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

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

### Step 4: Check the Solution
Now we should check our solution to make sure it is correct. We can do this by substituting \(x = 4\) back into the original equation.

Substituting \(x = 4\):

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

Calculating this:

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

Since both sides of the equation are equal, our solution checks out.

### Final Answer
Therefore, the solution to the equation \(5x + 8 + x = 32\) is

\[
\boxed{4}
\]

This shows all the steps taken to solve the equation and confirm that the solution is correct, demonstrating clear problem-solving skills.