Solve for X in 3x - 18 + 2x = 32: Linear Equation Practice

Q: What are like terms and how do I spot them?

Like terms have the same variable raised to the same power. In $ 3x - 18 + 2x = 32 $, both $ 3x $ and $ 2x $ are like terms because they both have x to the first power.

Q: Why can't I just solve for x in 3x first?

You need to simplify first! If you try to solve $ 3x = 32 + 18 - 2x $, you still have $ x $ on both sides. Combining like terms makes it much easier to isolate the variable.

Q: Can I move the 2x to the right side instead?

Yes, but it's usually more efficient to combine like terms on the same side first. Moving $ 2x $ to the right gives $ 3x - 18 = 32 - 2x $, then you'd need to add $ 2x $ to both sides anyway.

Q: How do I remember the order of operations for solving?

Follow this pattern: 1) Combine like terms, 2) Move constants, 3) Divide by coefficient. Think of it as cleaning up the equation step by step!

Linear Equations with Like Terms

$3x-18+2x=32$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Our goal is to find the value of X.

00:10 First, let's gather all the similar terms together.

00:15 Now, arrange the equation so that X is by itself on one side.

00:21 Once again, collect the terms as needed.

00:25 Great! Now isolate X completely.

00:29 And there you have it! That's the solution to our problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$3x-18+2x=32$

Step-by-step solution

To solve the equation $3x - 18 + 2x = 32$ , we begin by simplifying the left side:

Step 1: Combine like terms for the variable $x$ :
The terms involving $x$ are $3x$ and $2x$ . Combining them gives $5x$ . So the equation becomes $5x - 18 = 32$ .
Step 2: Isolate the term with the variable:
Add 18 to both sides of the equation to move the constant term to the right side:
$5x - 18 + 18 = 32 + 18$
This simplifies to $5x = 50$ .
Step 3: Solve for $x$ :
To isolate $x$ , divide both sides by 5:
$\frac{5x}{5} = \frac{50}{5}$
This simplifies to $x = 10$ .

Therefore, the solution to the equation is $\mathbf{x = 10}$ .

Final Answer

$10$

Key Points to Remember

Essential concepts to master this topic

Combining Like Terms: Add coefficients of same variables first
Technique: $3x + 2x = 5x$ before isolating the variable
Check: Substitute $x = 10$ : $3(10) - 18 + 2(10) = 32$ ✓

Common Mistakes

Avoid these frequent errors

Not combining like terms before solving
Don't solve $3x - 18 + 2x = 32$ by moving terms without combining first = confusing algebra! This leads to messy calculations and wrong answers. Always combine like terms on each side before isolating the variable.

Practice Quiz

Test your knowledge with interactive questions

$$ 5x=0 $$

FAQ

Everything you need to know about this question

What are like terms and how do I spot them?

Like terms have the same variable raised to the same power. In $3x - 18 + 2x = 32$ , both $3x$ and $2x$ are like terms because they both have x to the first power.

Why can't I just solve for x in 3x first?

You need to simplify first! If you try to solve $3x = 32 + 18 - 2x$ , you still have $x$ on both sides. Combining like terms makes it much easier to isolate the variable.

What if I get a different answer when I check?

If your check doesn't work, you made an error somewhere! Go back and carefully redo each step. The most common mistakes are arithmetic errors when combining like terms or adding/subtracting.

Can I move the 2x to the right side instead?

Yes, but it's usually more efficient to combine like terms on the same side first. Moving $2x$ to the right gives $3x - 18 = 32 - 2x$ , then you'd need to add $2x$ to both sides anyway.

How do I remember the order of operations for solving?

Follow this pattern: 1) Combine like terms, 2) Move constants, 3) Divide by coefficient. Think of it as cleaning up the equation step by step!

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