Solve the following linear equation for x. Then check your answer. Show all your steps for solving and checking. Make sure it looks like an 8th grader and put it into words.

Question

5x+8+x=32

Answer 1

Sure! Let's solve the equation step by step.

Step 1: Write down the equation

The equation we need to solve is:

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

Step 2: Combine like terms

In the equation, we notice that we have \(5x\) and \(x\). We can combine them to make it simpler.

So, \(5x + x\) is the same as \(6x\). Now, our equation looks like this:

\[ 6x + 8 = 32 \]

Step 3: Isolate the variable

Next, we want to get \(x\) by itself on one side of the equation. To do that, we need to get rid of the \(8\) that is being added to \(6x\).

We can do this by subtracting \(8\) from both sides of the equation:

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

This simplifies to:

\[ 6x = 24 \]

Step 4: Solve for \(x\)

Now, we need to solve for \(x\). Since \(6x\) means \(6\) times \(x\), we can find \(x\) by dividing both sides by \(6\):

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

This gives us:

\[ x = 4 \]

Step 5: Check the answer

To make sure our solution is correct, we can plug \(x = 4\) back into the original equation and see if both sides are equal.

Starting with the original equation:

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

Now, substitute \(x\) with \(4\):

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

Calculating the left side:

\[ 20 + 8 + 4 = 32 \]

Now add those up:

\[ 20 + 8 = 28 \]

Then adding \(4\):

\[ 28 + 4 = 32 \]

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

Conclusion

So the value of \(x\) is:

\[ \boxed{4} \]

And we verified that it satisfies the original equation!

Answer 2

Put it into words.

Answer 3

Sure! Let’s go through the solution again, but this time I’ll explain it in simple words.

Solving the Equation

First, we start with the equation we need to solve. It says:

Five times a number, plus eight, plus that same number equals thirty-two.

To make it easier, we can combine similar terms. I noticed that we have \(5x\) (which means five times our number) and \(x\) (which is one time our number). If we add those together, \(5x + x\), that gives us \(6x\). So now our equation looks like this:

Six times a number plus eight equals thirty-two.

Next, we want to find out what this number is, so we need to get that number by itself on one side of the equation. The first thing we can do is get rid of the \(8\) that’s added to \(6x\). Since \(8\) is being added, the opposite operation is to subtract \(8\). So, we subtract \(8\) from both sides of the equation:

Six times a number equals twenty-four.

Now, to find the number, we need to divide both sides by \(6\) because \(6x\) means six times the number. So when we divide \(24\) by \(6\), we get:

The number equals four.

Checking the Answer

Now that we found that our number is \(4\), we want to make sure we did it right. To check our answer, we can take \(4\) and put it back into the original equation:

Five times four, plus eight, plus four.

Let’s calculate that step by step. First, five times four is \(20\). Then we add \(8\) to \(20\), which gives us \(28\). Finally, we add the last \(4\):

Twenty-eight plus four equals thirty-two.

Since both sides of the equation are equal (we get \(32\) on both sides), we know our answer is correct.

Conclusion

So, we found that the number we were looking for is:

Four.

And we confirmed it by checking that it works in the original equation!

Answer 4

Make it shorter

Answer 5

Sure! Here’s a shorter version of the explanation:

Solving the Equation

We start with the equation:

Five times a number plus eight plus that same number equals thirty-two.

First, we combine \(5x\) and \(x\) to get \(6x\):

Six times a number plus eight equals thirty-two.

Next, we subtract \(8\) from both sides to isolate the \(6x\):

Six times a number equals twenty-four.

Now, we divide both sides by \(6\) to find our number:

The number equals four.

Checking the Answer

To make sure our answer is right, we plug \(4\) back into the original equation:

Five times four plus eight plus four.

Calculating that, we get:

20 + 8 + 4 equals 32.

Since both sides are equal, our answer is confirmed.

Conclusion

So, the number we found is:

Four.

Answer 6

NOW put it into a sentence

Answer 7

I solved the equation \(5x + 8 + x = 32\) by combining like terms to get \(6x + 8 = 32\), subtracting \(8\) to find \(6x = 24\), and then dividing by \(6\) to find that \(x = 4\), and I confirmed this solution by substituting \(4\) back into the original equation, which showed that both sides equal \(32\).