Solve Linear Equation: 4y-7+6y=3-10y for Variable y

Q: Why do I need to combine like terms first?

Combining like terms simplifies the equation before you start moving variables around. It's much easier to work with $ 10y - 7 = 3 - 10y $ than the original messy equation!

Q: Which side should I move all the variables to?

It doesn't matter! Choose the side that will give you a positive coefficient for the variable. In this problem, moving everything to the left gives us $ 20y $, which is positive and easy to work with.

Q: What if I get a negative coefficient for y?

No problem! Just divide by the negative number. For example, if you get $ -20y = -10 $, then $ y = \frac{-10}{-20} = \frac{1}{2} $.

Q: How do I know when to add or subtract terms?

Remember: to move a term across the equals sign, do the opposite operation. If you see $ -10y $ on the right, add $ +10y $ to both sides to move it left.

Q: Can I check my answer a different way?

Yes! Besides substituting back, you can also work backwards. Start with $ y = \frac{1}{2} $ and build up both sides of the original equation step by step.

Linear Equations with Variable Consolidation

$4y-7+6y=3-10y$

$y=?$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Collect terms

00:12 We want to isolate the unknown Y

00:18 Let's arrange the equation so that Y is only on one side

00:28 Collect terms

00:36 Isolate the unknown Y

00:42 Factorize 20 into 10 and 2

00:48 Reduce what we can

00:51 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

$4y-7+6y=3-10y$

$y=?$

Step-by-step solution

To solve the equation $4y - 7 + 6y = 3 - 10y$ , follow these steps:

Step 1: Combine like terms on both sides of the equation.

The left side simplifies by combining the $y$ -terms:
$4y + 6y - 7 = 10y - 7$ .

On the right side, there is one $y$ -term, but we can leave it for the next steps.

Step 2: Isolate the $y$ -terms.

Add $10y$ to both sides to move all $y$ -terms to the left side:

$10y - 7 + 10y = 3$

Simplifying the left side, we get:

$20y - 7 = 3$

Step 3: Isolate $y$ .

Add $7$ to both sides to eliminate the constant term on the left:

$20y = 3 + 7$

$20y = 10$

Divide both sides by $20$ to solve for $y$ :

$y = \frac{10}{20}$

$y = \frac{1}{2}$

Therefore, the solution to the problem is $y = \frac{1}{2}$ .

Final Answer

$\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Rule: Combine like terms before moving variables to one side
Technique: 4y + 6y = 10y, then add 10y to get 20y
Check: Substitute $y = \frac{1}{2}$ : 10(1/2) - 7 = 3 - 10(1/2) gives -2 = -2 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to combine like terms on the same side
Don't solve 4y - 7 + 6y = 3 - 10y by immediately moving variables without combining 4y + 6y = wrong answer! This creates unnecessary complexity and calculation errors. Always combine like terms on each side first, then move all variables to one side.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 3x=18 $$

FAQ

Everything you need to know about this question

Why do I need to combine like terms first?

Combining like terms simplifies the equation before you start moving variables around. It's much easier to work with $10y - 7 = 3 - 10y$ than the original messy equation!

Which side should I move all the variables to?

It doesn't matter! Choose the side that will give you a positive coefficient for the variable. In this problem, moving everything to the left gives us $20y$ , which is positive and easy to work with.

What if I get a negative coefficient for y?

No problem! Just divide by the negative number. For example, if you get $-20y = -10$ , then $y = \frac{-10}{-20} = \frac{1}{2}$ .

How do I know when to add or subtract terms?

Remember: to move a term across the equals sign, do the opposite operation. If you see $-10y$ on the right, add $+10y$ to both sides to move it left.

Can I check my answer a different way?

Yes! Besides substituting back, you can also work backwards. Start with $y = \frac{1}{2}$ and build up both sides of the original equation step by step.

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Solve Linear Equation: 4y-7+6y=3-10y for Variable y

Linear Equations with Variable Consolidation

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I need to combine like terms first?

Which side should I move all the variables to?

What if I get a negative coefficient for y?

How do I know when to add or subtract terms?

Can I check my answer a different way?

🌟 Unlock Your Math Potential

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