Solve the following linear equation for x. Then check your answer. Show all your steps for solving and checking.

Question

5x + 8 + x = 32

Answer 1

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 2

make it shorter

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:

\[ \boxed{4} \]