Solve the following linear equation for x. Then check your answer. Show all your steps for solving and checking. Make sure it is an actual equation that is readable to a normal person.

5x+8+x=32

3 answers

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

Step 1: Combine like terms.

The equation has two terms with \( x \): \( 5x \) and \( x \). We can combine them:

\[ 5x + x = 6x \]

Now, 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 of the equation:

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

This simplifies to:

\[ 6x = 24 \]

Step 3: Solve for \( x \).

Now, divide both sides of the equation by 6:

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

This simplifies to:

\[ x = 4 \]

Step 4: Check the solution.

Now, we will verify our solution by substituting \( x = 4 \) back into the original equation:

The original equation is:

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

Substituting \( x = 4 \):

\[ 5(4) + 8 + 4 = 32 \]

Calculate the left-hand side:

\[ 20 + 8 + 4 = 32 \]

Now we add:

\[ 20 + 8 = 28 \] \[ 28 + 4 = 32 \]

Since both sides of the equation are equal (32 = 32), our solution is confirmed.

Final Answer:

\[ x = 4 \]

So put it into one equation

Certainly! The original equation can be solved step by step, but if you want the entire solution condensed into one equation form, we can frame it like this:

Starting from the original equation:

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

Combine like terms:

\[ 6x + 8 = 32 \]

Isolate the variable:

\[ 6x = 32 - 8 \]

Simplify:

\[ 6x = 24 \]

Now, divide both sides by 6:

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

Finally, simplify to get the answer:

\[ x = 4 \]

As one complete equation form, it can be represented as:

\[ x = \frac{32 - 8}{6} = 4 \]