Solve Linear Equation: Finding X in 3x - x = 8

Q: What does 'like terms' mean exactly?

Like terms are terms with the same variable raised to the same power. In $ 3x - x $, both terms have the variable x to the first power, so they're like terms!

Q: Why can't I just divide both sides by 3 right away?

Because you have two different terms on the left: 3x and -x. You must combine them first to get 2x, then divide by 2, not 3.

Q: How do I combine 3x - x step by step?

Think of it as: $ 3x - 1x = (3-1)x = 2x $. You're subtracting the coefficients (the numbers in front) and keeping the variable x.

Q: What if I had 3x + x instead?

Then you'd add the coefficients: $ 3x + 1x = (3+1)x = 4x $. The same rule applies - combine the numbers, keep the variable!

Q: How can I check if x = 4 is really correct?

Substitute 4 for x in the original equation: $ 3(4) - 4 = 12 - 4 = 8 $. Since this equals 8, your answer is correct!

Linear Equations with Like Terms

$3x - x = 8$

$x = \text{?}$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$3x - x = 8$

$x = \text{?}$

Step-by-step solution

Start by simplifying the left-hand side of the equation:

$3x - x = 2x$

So the equation becomes:

$2x = 8$

To find the value of $x$ , divide both sides by 2:

$x = \frac{8}{2}$

Then simplify the fraction:

$x = 4$

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

Final Answer

Key Points to Remember

Essential concepts to master this topic

Combining Like Terms: Subtract coefficients of same variables (3x - x = 2x)
Technique: Simplify left side first: 3x - x = 2x, then solve 2x = 8
Check: Substitute back: 3(4) - 4 = 12 - 4 = 8 ✓

Common Mistakes

Avoid these frequent errors

Trying to solve without combining like terms first
Don't jump straight to dividing by 3 or subtracting x from both sides = wrong answer! This skips the essential step of simplifying. Always combine like terms on each side before isolating the variable.

Practice Quiz

Test your knowledge with interactive questions

Find the value of the parameter X

$\frac{1}{3}x=\frac{1}{9}$

FAQ

Everything you need to know about this question

What does 'like terms' mean exactly?

Like terms are terms with the same variable raised to the same power. In $3x - x$ , both terms have the variable x to the first power, so they're like terms!

Why can't I just divide both sides by 3 right away?

Because you have two different terms on the left: 3x and -x. You must combine them first to get 2x, then divide by 2, not 3.

How do I combine 3x - x step by step?

Think of it as: $3x - 1x = (3-1)x = 2x$ . You're subtracting the coefficients (the numbers in front) and keeping the variable x.

What if I had 3x + x instead?

Then you'd add the coefficients: $3x + 1x = (3+1)x = 4x$ . The same rule applies - combine the numbers, keep the variable!

How can I check if x = 4 is really correct?

Substitute 4 for x in the original equation: $3(4) - 4 = 12 - 4 = 8$ . Since this equals 8, your answer is correct!

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