Solve for Y in the Equation y+10-3y=-150: Linear Equation Practice

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

Like terms have the same variable with the same exponent. In $ y + 10 - 3y $, both y and -3y are like terms. Combining them simplifies the equation and makes it easier to solve!

Q: How do I combine y and -3y correctly?

Think of it as $ 1y + (-3y) = -2y $. The coefficients are 1 and -3, so 1 + (-3) = -2. This gives us $ -2y $.

Q: Why do I subtract 10 from both sides instead of adding?

We have $ -2y + 10 = -150 $. To isolate the $ -2y $ term, we need to eliminate the +10. The opposite of +10 is -10, so we subtract 10 from both sides.

Q: When I divide by -2, why does the answer become positive?

We have $ -2y = -160 $. When dividing: $ \frac{-160}{-2} = 80 $. Remember: negative divided by negative equals positive!

Q: How can I check if y = 80 is really correct?

Substitute into the original equation: $ 80 + 10 - 3(80) = 80 + 10 - 240 = -150 $. Since this equals -150, our answer is correct!

Linear Equations with Like Terms

$y+10-3y=-150$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find Y

00:03 Collect terms

00:10 Arrange the equation so that only the unknown Y is on one side

00:16 Isolate Y

00:19 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

$y+10-3y=-150$

Step-by-step solution

To solve the equation $y + 10 - 3y = -150$ , follow these steps:

Step 1: Combine like terms on the left side of the equation:

$y + 10 - 3y$ simplifies to $-2y + 10$ .

Now the equation is:

$-2y + 10 = -150$ .

Step 2: Subtract 10 from both sides to begin isolating $-2y$ :

$-2y + 10 - 10 = -150 - 10$ .

This simplifies to:

$-2y = -160$ .

Step 3: Divide both sides by $-2$ to solve for $y$ :

$\frac{-2y}{-2} = \frac{-160}{-2}$ .

Thus, $y = 80$ .

Therefore, the solution to the problem is $y = 80$ .

Final Answer

$80$

Key Points to Remember

Essential concepts to master this topic

Combine Like Terms: Group y-terms together before solving for variable
Technique: $y - 3y = -2y$ when combining coefficients
Check: Substitute $y = 80$ : $80 + 10 - 240 = -150$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to combine like terms first
Don't try to isolate y without combining like terms = confusing multiple y-terms! This leads to algebraic errors and wrong solutions. Always combine all like terms on each side before moving terms across the equals sign.

Practice Quiz

Test your knowledge with interactive questions

$$ -16+a=-17 $$

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 $y + 10 - 3y$ , both y and -3y are like terms. Combining them simplifies the equation and makes it easier to solve!

How do I combine y and -3y correctly?

Think of it as $1y + (-3y) = -2y$ . The coefficients are 1 and -3, so 1 + (-3) = -2. This gives us $-2y$ .

Why do I subtract 10 from both sides instead of adding?

We have $-2y + 10 = -150$ . To isolate the $-2y$ term, we need to eliminate the +10. The opposite of +10 is -10, so we subtract 10 from both sides.

When I divide by -2, why does the answer become positive?

We have $-2y = -160$ . When dividing: $\frac{-160}{-2} = 80$ . Remember: negative divided by negative equals positive!

How can I check if y = 80 is really correct?

Substitute into the original equation: $80 + 10 - 3(80) = 80 + 10 - 240 = -150$ . Since this equals -150, our answer is correct!

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