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Solve the following linear equations for X. The check

your answer. Show all of your steps for solving and checking.

5x + 8 + x = 32

7 answers

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

Step 1: Combine like terms

First, we can combine the terms with \( x \) on the left side of the equation:

\[ 5x + x = 6x \]

So the equation becomes:

\[ 6x + 8 = 32 \]

Step 2: Subtract 8 from both sides

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: Divide both sides by 6

Now, we will divide both sides by 6 to solve for \( x \):

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

This gives us:

\[ x = 4 \]

Step 4: Check the solution

To verify our solution, we will substitute \( x = 4 \) back into the original equation to see if both sides are equal:

The original equation is:

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

Substituting \( x = 4 \):

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

Calculating the left side:

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

Since both sides of the equation are equal, our solution \( x = 4 \) is confirmed to be correct.

Final Answer

\[ x = 4 \]

Make it like a 8th grader wrote it

Sure! Here’s how an 8th grader might write the solution:

Problem: Solve the equation 5x + 8 + x = 32.

Step 1: Combine like terms.

First, I see that there are two \( x \) terms on the left. I can combine them:

\[ 5x + x = 6x \]

So now the equation looks like this:

\[ 6x + 8 = 32 \]

Step 2: Get \( x \) by itself.

Next, I want to get rid of the \( 8 \) on the left side. I do that 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, I need to find out what \( x \) is. I will divide by \( 6 \) because I have \( 6x \):

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

When I do the division, I get:

\[ x = 4 \]

Step 4: Check my answer.

Now I should check if \( x = 4 \) makes the original equation true. I’ll plug \( 4 \) back into the original equation:

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

Calculating this gives:

\[ 20 + 8 + 4 = 32 \]

Adding it all up:

\[ 20 + 8 = 28 \quad \text{and then} \quad 28 + 4 = 32 \]

Since both sides equal \( 32 \), my answer is correct!

Final Answer: \( x = 4 \)

That’s how I solved the problem!

Take these * out and make it in categories and in order but all right

Sure! Here’s a well-organized version of the solution with the steps in categories and order, presented clearly:

Problem

Solve the equation:
5x + 8 + x = 32

Steps to Solve

Step 1: Combine Like Terms

  • Combine the \( x \) terms on the left side: \[ 5x + x = 6x \]
  • Now the equation looks like: \[ 6x + 8 = 32 \]

Step 2: Isolate the \( x \) Term

  • Subtract \( 8 \) from both sides to get rid of the constant: \[ 6x + 8 - 8 = 32 - 8 \]
  • This simplifies to: \[ 6x = 24 \]

Step 3: Solve for \( x \)

  • Divide both sides by \( 6 \): \[ x = \frac{24}{6} \]
  • This gives: \[ x = 4 \]

Check the Solution

To verify that \( x = 4 \) is correct, substitute \( 4 \) back into the original equation:

  • Original equation: \[ 5x + 8 + x = 32 \]
  • Substitute \( x = 4 \): \[ 5(4) + 8 + 4 = 32 \]
  • Calculate each part: \[ 20 + 8 + 4 = 32 \]
  • Simplifying: \[ 20 + 8 = 28 \quad \text{and} \quad 28 + 4 = 32 \]
  • Since both sides equal \( 32 \), the solution is confirmed to be correct!

Final Answer

\( x = 4 \)

This format presents the solution in a clear and organized way, making it easy to follow each step.

Now take the Hashtags out

Of course! Here’s the solution presented without hashtags but still organized and clear:

Problem
Solve the equation:
5x + 8 + x = 32

Steps to Solve

Step 1: Combine Like Terms

  • Combine the \( x \) terms on the left side:
    \[
    5x + x = 6x
    \]
  • Now the equation looks like:
    \[
    6x + 8 = 32
    \]

Step 2: Isolate the \( x \) Term

  • Subtract \( 8 \) from both sides to get rid of the constant:
    \[
    6x + 8 - 8 = 32 - 8
    \]
  • This simplifies to:
    \[
    6x = 24
    \]

Step 3: Solve for \( x \)

  • Divide both sides by \( 6 \):
    \[
    x = \frac{24}{6}
    \]
  • This gives:
    \[
    x = 4
    \]

Check the Solution
To verify that \( x = 4 \) is correct, substitute \( 4 \) back into the original equation:

  • Original equation:
    \[
    5x + 8 + x = 32
    \]
  • Substitute \( x = 4 \):
    \[
    5(4) + 8 + 4 = 32
    \]
  • Calculate each part:
    \[
    20 + 8 + 4 = 32
    \]
  • Simplifying:
    \[
    20 + 8 = 28 \quad \text{and} \quad 28 + 4 = 32
    \]
  • Since both sides equal \( 32 \), the solution is confirmed to be correct!

Final Answer
\( x = 4 \)

This format ensures that each part of the solution is easy to read and follow.