Solve the Linear Equation: 2+4y-2y=4 Step-by-Step

Q: What are like terms exactly?

Like terms have the exact same variable part! In this problem, $ 4y $ and $ 2y $ are like terms because they both have 'y'. The constant 2 is different since it has no variable.

Q: Why do I combine 4y - 2y instead of 4y + 2y?

Look carefully at the signs! The equation is $ 2 + 4y - 2y = 4 $, which means you're subtracting 2y. So $ 4y - 2y = 2y $, not $ 4y + 2y = 6y $.

Q: Can I move terms to the other side instead of combining first?

You could, but it's much more complicated! Moving $ 4y $ and $ 2y $ separately creates extra steps. Always combine like terms first to simplify your work.

Q: How do I check if y = 1 is really correct?

Substitute y = 1 into the original equation: $ 2 + 4(1) - 2(1) = 2 + 4 - 2 = 4 $. Since the left side equals 4, and the right side is 4, your answer is correct!

Q: What if I get a different answer like y = 3?

Check it! Substitute: $ 2 + 4(3) - 2(3) = 2 + 12 - 6 = 8 $. Since 8 ≠ 4, this would be wrong. Always verify by substituting back into the original equation.

Linear Equations with Like Term Combining

$2+4y-2y=4$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find Y

00:04 Collect terms

00:11 Arrange the equation so that only the unknown Y is on one side

00:14 Collect terms

00:17 Isolate Y

00:20 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

$2+4y-2y=4$

Step-by-step solution

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

Step 1: Combine like terms.
Step 2: Simplify and isolate the variable.
Step 3: Solve for the variable.

Let's address each step in detail:
Step 1: Combine the like terms on the left side of the equation.
The original equation is: $2 + 4y - 2y = 4$ Combine the terms involving $y$ :
$4y - 2y = 2y$ The equation now becomes:
$2 + 2y = 4$ Step 2: Simplify the equation to isolate $2y$ .
Subtract 2 from both sides to begin the process of isolating $y$ :
$2y = 4 - 2$ Simplify the right side:
$2y = 2$ Step 3: Solve for $y$ by dividing both sides by 2:
$y = \frac{2}{2}$ This simplifies to:
$y = 1$ Thus, the solution to the equation is: $y = 1$ .

Final Answer

$1$

Key Points to Remember

Essential concepts to master this topic

Combine Like Terms: Collect all variables with same variable part first
Technique: Simplify $4y - 2y = 2y$ before isolating variable
Check: Substitute back: $2 + 4(1) - 2(1) = 4$ ✓

Common Mistakes

Avoid these frequent errors

Not combining like terms before isolating the variable
Don't try to isolate y from 2 + 4y - 2y = 4 without combining first = confusing algebra steps! This leads to more complex calculations and potential errors. Always combine like terms (4y - 2y = 2y) to get 2 + 2y = 4 before isolating.

Practice Quiz

Test your knowledge with interactive questions

$$ x+x=8 $$

FAQ

Everything you need to know about this question

What are like terms exactly?

Like terms have the exact same variable part! In this problem, $4y$ and $2y$ are like terms because they both have 'y'. The constant 2 is different since it has no variable.

Why do I combine 4y - 2y instead of 4y + 2y?

Look carefully at the signs! The equation is $2 + 4y - 2y = 4$ , which means you're subtracting 2y. So $4y - 2y = 2y$ , not $4y + 2y = 6y$ .

Can I move terms to the other side instead of combining first?

You could, but it's much more complicated! Moving $4y$ and $2y$ separately creates extra steps. Always combine like terms first to simplify your work.

How do I check if y = 1 is really correct?

Substitute y = 1 into the original equation: $2 + 4(1) - 2(1) = 2 + 4 - 2 = 4$ . Since the left side equals 4, and the right side is 4, your answer is correct!

What if I get a different answer like y = 3?

Check it! Substitute: $2 + 4(3) - 2(3) = 2 + 12 - 6 = 8$ . Since 8 ≠ 4, this would be wrong. Always verify by substituting back into the original equation.

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