Solve the Linear Equation: Finding X in x + x = 8

Q: Why can't I just divide 8 by 2 right away?

You need to combine like terms first! The equation $ x + x = 8 $ has two x terms on the left side that must be added together to get $ 2x = 8 $ before dividing.

Q: What does 'like terms' mean exactly?

Like terms have the same variable with the same power. Since both terms are just x (which is $ x^1 $), they can be combined: $ x + x = 2x $.

Q: How do I know when to combine terms vs. when to divide?

Always simplify first, solve second! If you see the same variable terms that can be combined (like $ x + x $), combine them first. Then use inverse operations to solve.

Q: Is x + x always equal to 2x?

Yes! $ x + x $ always equals $ 2x $, just like $ 3 + 3 = 6 $ or $ 5 + 5 = 10 $. When you have identical terms, you're adding their coefficients: $ 1x + 1x = 2x $.

Linear Equations with Combining Like Terms

$x+x=8$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's find the value of X.

00:08 First, gather all the factors.

00:12 Next, isolate X on one side.

00:16 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$x+x=8$

Step-by-step solution

To solve the equation $x + x = 8$ , follow these steps:

Step 1: Combine like terms. Since the left side of the equation is $x + x$ , it can be simplified to $2x$ . This gives us the equation $2x = 8$ .
Step 2: Solve for $x$ by isolating it. Divide both sides of the equation by 2 to get $x$ .
Performing the division gives $x = \frac{8}{2}$ .
Step 3: Calculate the result of the division. $\frac{8}{2} = 4$ .

Therefore, the solution to the equation is $x = 4$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Combine like terms first to simplify the equation
Technique: $x + x$ becomes $2x$ , then divide: $\frac{8}{2} = 4$
Check: Substitute back: $4 + 4 = 8$ ✓

Common Mistakes

Avoid these frequent errors

Solving without combining like terms first
Don't try to solve $x + x = 8$ by dividing both sides by 2 immediately = confusion and wrong setup! This skips the crucial step of recognizing that $x + x$ equals $2x$ . Always combine like terms first to get $2x = 8$ , then solve.

Practice Quiz

Test your knowledge with interactive questions

$$ -16+a=-17 $$

FAQ

Everything you need to know about this question

Why can't I just divide 8 by 2 right away?

You need to combine like terms first! The equation $x + x = 8$ has two x terms on the left side that must be added together to get $2x = 8$ before dividing.

What does 'like terms' mean exactly?

Like terms have the same variable with the same power. Since both terms are just x (which is $x^1$ ), they can be combined: $x + x = 2x$ .

How do I know when to combine terms vs. when to divide?

Always simplify first, solve second! If you see the same variable terms that can be combined (like $x + x$ ), combine them first. Then use inverse operations to solve.

Is x + x always equal to 2x?

Yes! $x + x$ always equals $2x$ , just like $3 + 3 = 6$ or $5 + 5 = 10$ . When you have identical terms, you're adding their coefficients: $1x + 1x = 2x$ .

What if I get a different answer when I check?

If substituting your answer doesn't work, go back and check your combining step. Make sure $x + x$ became $2x$ , not something else!

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