Solve Linear Equation: Finding Y in 2y-5y+12+30=0

Q: What are like terms and why do I combine them?

Like terms have the same variable with the same exponent. In $ 2y - 5y $, both terms have y, so they combine to $ -3y $. This simplifies the equation and makes it easier to solve!

Q: Why is 2y - 5y equal to -3y and not 3y?

Think of it as $ (+2)y + (-5)y $. When you add +2 and -5, you get -3. So $ 2y - 5y = -3y $. The subtraction sign makes the 5y negative!

Q: What if I get a negative answer? Is that wrong?

Negative answers are completely normal! In this problem, we got a positive answer (14), but many equations have negative solutions. Always check your work by substituting back into the original equation.

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

You could, but combining like terms first makes the equation much simpler to work with. It's like cleaning up your workspace before starting the main task!

Q: How do I check if y = 14 is really correct?

Substitute y = 14 into the original equation: $ 2(14) + 12 - 5(14) + 30 = 28 + 12 - 70 + 30 = 0 $. Since we get 0, our answer is correct!

Linear Equations with Like Term Combination

$2y+12-5y+30=0$

$y=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's solve the problem together.

00:11 First, we need to find the value of Y.

00:15 Let's group similar terms to simplify it.

00:22 We'll move everything except Y to one side of the equation.

00:31 Now, Y is all by itself. Great job!

00:42 And that's how we solve for Y. Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$2y+12-5y+30=0$

$y=\text{?}$

Step-by-step solution

To solve the equation $2y + 12 - 5y + 30 = 0$ , follow these steps:

Step 1: Simplify the equation by combining like terms.
Combine the $y$ terms and the constant terms:
$2y - 5y + 12 + 30 = 0$
Step 2: Calculate the combined terms.
$2y - 5y = -3y$
$12 + 30 = 42$
Thus, the equation becomes:
$-3y + 42 = 0$
Step 3: Isolate the variable $y$ .
Subtract 42 from both sides to get:
$-3y = -42$
Step 4: Solve for $y$ by dividing both sides by $-3$ :
$y = \frac{-42}{-3}$
Step 5: Simplify the fraction:
$y = 14$

Therefore, the solution to the equation is $y = 14$ .

Final Answer

$14$

Key Points to Remember

Essential concepts to master this topic

Combining Terms: Group all y terms together and all constants together
Technique: Calculate $2y - 5y = -3y$ and $12 + 30 = 42$
Check: Substitute y = 14: $2(14) - 5(14) + 12 + 30 = 0$ ✓

Common Mistakes

Avoid these frequent errors

Combining unlike terms or making sign errors
Don't combine y terms with constant terms or forget negative signs = wrong coefficients! This leads to incorrect simplified equations like -3y + 12 = 0 instead of -3y + 42 = 0. Always combine only like terms and carefully track positive and negative signs.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 5x=25 $$

FAQ

Everything you need to know about this question

What are like terms and why do I combine them?

Like terms have the same variable with the same exponent. In $2y - 5y$ , both terms have y, so they combine to $-3y$ . This simplifies the equation and makes it easier to solve!

Why is 2y - 5y equal to -3y and not 3y?

Think of it as $(+2)y + (-5)y$ . When you add +2 and -5, you get -3. So $2y - 5y = -3y$ . The subtraction sign makes the 5y negative!

How do I know which terms to combine first?

It doesn't matter! You can combine the y terms first or the constants first. In this problem:

y terms: $2y - 5y = -3y$
Constants: $12 + 30 = 42$

Both approaches give you

-3y + 42 = 0

What if I get a negative answer? Is that wrong?

Negative answers are completely normal! In this problem, we got a positive answer (14), but many equations have negative solutions. Always check your work by substituting back into the original equation.

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

You could, but combining like terms first makes the equation much simpler to work with. It's like cleaning up your workspace before starting the main task!

How do I check if y = 14 is really correct?

Substitute y = 14 into the original equation: $2(14) + 12 - 5(14) + 30 = 28 + 12 - 70 + 30 = 0$ . Since we get 0, our answer is correct!

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