Solve for X: Simplifying 4x + 2x = 18 Step by Step

Q: What exactly are 'like terms'?

Like terms are terms with the same variable raised to the same power. In this case, both 4x and 2x have the variable x raised to the first power, so they're like terms!

Q: Why can I add 4x and 2x but not 4x and 2y?

You can only combine terms with identical variable parts. Since 4x and 2x both have just 'x', you add the numbers: 4 + 2 = 6x. But 4x and 2y have different variables, so they stay separate.

Q: What if I have 4x + 2x + 3?

Combine only the like terms! 4x + 2x = 6x, but the 3 has no variable, so it stays separate. Your simplified expression would be 6x + 3.

Q: How do I know when to stop combining terms?

Stop when you have one term for each different variable type. In our example, after getting 6x = 18, there's only one x-term on each side, so you're ready to solve!

Q: Can I combine terms across the equals sign?

No! Only combine like terms on the same side of the equation. The equals sign creates a boundary - keep left side and right side separate until you're ready to solve.

Linear Equations with Like Terms

$4x + 2x = 18$

Solve the equation above for $x$ .

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$4x + 2x = 18$

Solve the equation above for $x$ .

Step-by-step solution

Combine like terms on the left-hand side:

$4x + 2x = 6x$

The equation becomes:

$6x = 18$

Divide both sides by 6 to solve for $x$ :

$x = \frac{18}{6}$

Simplify the division:

$x = 3$

Thus, $x = 3$ is the solution to the equation.

Final Answer

$x = 3$

Key Points to Remember

Essential concepts to master this topic

Combine Like Terms: Add coefficients of variables with same power
Technique: 4x + 2x becomes 6x by adding 4 + 2
Check: Substitute x = 3: 4(3) + 2(3) = 12 + 6 = 18 ✓

Common Mistakes

Avoid these frequent errors

Adding variables instead of coefficients
Don't add 4x + 2x = 6x² by multiplying the x's! This creates a quadratic equation when you should have a linear one. Always add only the coefficients: 4 + 2 = 6, keeping the variable as x.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 5x=25 $$

FAQ

Everything you need to know about this question

What exactly are 'like terms'?

Like terms are terms with the same variable raised to the same power. In this case, both 4x and 2x have the variable x raised to the first power, so they're like terms!

Why can I add 4x and 2x but not 4x and 2y?

You can only combine terms with identical variable parts. Since 4x and 2x both have just 'x', you add the numbers: 4 + 2 = 6x. But 4x and 2y have different variables, so they stay separate.

What if I have 4x + 2x + 3?

Combine only the like terms! 4x + 2x = 6x, but the 3 has no variable, so it stays separate. Your simplified expression would be 6x + 3.

How do I know when to stop combining terms?

Stop when you have one term for each different variable type. In our example, after getting 6x = 18, there's only one x-term on each side, so you're ready to solve!

Can I combine terms across the equals sign?

No! Only combine like terms on the same side of the equation. The equals sign creates a boundary - keep left side and right side separate until you're ready to solve.

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