Solve the following linear equation for x

Question

. Then check your answer. Show all your steps for solving and checking.

5x+8+x=32

Answer 1

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

Step 1: Combine like terms

First, we combine the \( x \) terms on the left side of the equation.

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

This simplifies to:

\[ 6x + 8 = 32 \]

Step 2: Isolate the term with \( x \)

Next, we want to isolate the \( x \) term. We can do this by subtracting 8 from both sides of the equation:

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

This simplifies to:

\[ 6x = 24 \]

Step 3: Solve for \( x \)

Now, to find \( x \), divide both sides by 6:

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

This simplifies to:

\[ x = 4 \]

Step 4: Check the solution

To verify the solution, we can 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:

\[ 20 + 8 + 4 = 32 \]

Simplifying:

\[ 32 = 32 \]

Since both sides of the equation are equal, our solution is verified.

Final Answer

Thus, the solution to the equation \( 5x + 8 + x = 32 \) is:

\[ \boxed{4} \]

Answer 2

can you make it smaller

Answer 3

Sure! Here’s a more concise version of the solution:

Given Equation:
\[ 5x + 8 + x = 32 \]

Step 1: Combine like terms

\[ 6x + 8 = 32 \]

Step 2: Isolate \( x \)

Subtract 8 from both sides: \[ 6x = 24 \]

Step 3: Solve for \( x \)

Divide by 6: \[ x = 4 \]

Step 4: Check the solution

Substitute \( x = 4 \) back into the original equation: \[ 5(4) + 8 + 4 = 32 \] \[ 20 + 8 + 4 = 32 \] \[ 32 = 32 \] (True)

Final Answer

\[ \boxed{4} \]