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

1 answer

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

\[ x = 4 \]