Solve for X in the Linear Equation x + 2x = 9

Q: Why do I combine x + 2x first instead of solving right away?

You need to simplify before solving! Think of x as 1x, so you have 1x + 2x = 3x. This gives you one clean term to work with instead of multiple x terms.

Q: What does 'like terms' actually mean?

Like terms have the same variable with the same power. Since both x and 2x have the variable x to the first power, they're like terms and can be combined.

Q: Can I solve this equation differently?

Yes! You could distribute first: $ x + 2x = 9 $ becomes $ x = 9 - 2x $, then $ 3x = 9 $. But combining like terms first is usually faster!

Q: What if I get a different number when checking my answer?

If your check doesn't work, go back and look for arithmetic errors. Make sure you combined like terms correctly (1 + 2 = 3) and divided both sides by the same number.

Linear Equations with Like Terms

$x+2x=9$

$x=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Collect terms

00:06 We want to isolate the unknown X

00:11 Let's isolate the unknown X

00:19 Let's reduce as much as possible

00:24 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$x+2x=9$

$x=\text{?}$

Step-by-step solution

To solve this problem, we'll follow these steps:

Combine like terms on the left side of the equation.
Solve for $x$ by isolating it on one side of the equation.

Let's work through the solution:

Step 1: Combine like terms in the equation $x + 2x = 9$ . The terms $x$ and $2x$ are like terms because they both contain the variable $x$ . When combined, these terms give us:

$x + 2x = 3x$

Step 2: The equation now simplifies to:

$3x = 9$

Step 3: Solve for $x$ by dividing both sides of the equation by 3 to isolate $x$ :

$x = \frac{9}{3}$

The calculation gives us:

$x = 3$

Therefore, the solution to the problem is $x = 3$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Combine like terms first before solving for the variable
Technique: Add coefficients: x + 2x = 3x, then divide both sides by 3
Check: Substitute 3 back: 3 + 2(3) = 3 + 6 = 9 ✓

Common Mistakes

Avoid these frequent errors

Adding x and 2x incorrectly
Don't think x + 2x = 2x = wrong answer! This ignores the first x term completely. Always add the coefficients: 1x + 2x = 3x before dividing.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 5x=25 $$

FAQ

Everything you need to know about this question

Why do I combine x + 2x first instead of solving right away?

You need to simplify before solving! Think of x as 1x, so you have 1x + 2x = 3x. This gives you one clean term to work with instead of multiple x terms.

What does 'like terms' actually mean?

Like terms have the same variable with the same power. Since both x and 2x have the variable x to the first power, they're like terms and can be combined.

How do I know what coefficient to use for just x?

When you see just x by itself, it has an invisible coefficient of 1. So x is really 1x, making it easy to add: 1x + 2x = 3x.

Can I solve this equation differently?

Yes! You could distribute first: $x + 2x = 9$ becomes $x = 9 - 2x$ , then $3x = 9$ . But combining like terms first is usually faster!

What if I get a different number when checking my answer?

If your check doesn't work, go back and look for arithmetic errors. Make sure you combined like terms correctly (1 + 2 = 3) and divided both sides by the same number.

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