Solve Linear Equation: 12y+3y-10+7(y-4)=2y Step-by-Step

Q: Why do I need to distribute 7 to both y and -4?

The distributive property says you must multiply the outside number by every term inside the parentheses. So $ 7(y - 4) = 7 \times y + 7 \times (-4) = 7y - 28 $.

Q: How do I combine like terms correctly?

Look for terms with the same variable and power. Here, combine all the y terms: $ 12y + 3y + 7y = 22y $, and combine constants: $ -10 + (-28) = -38 $.

Q: How do I move terms to isolate y?

Use inverse operations. To move $ 2y $ from the right side, subtract it from both sides: $ 22y - 2y = 38 $. This gives you $ 20y = 38 $.

Q: Why do I divide by 20 at the end?

To isolate y, you need to undo the multiplication by 20. Since $ 20y = 38 $, divide both sides by 20: $ y = \frac{38}{20} = 1.9 $.

Linear Equations with Distributive Property

$12y+3y-10+7(y-4)=2y$

$y=?$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solution

00:04 Open parentheses properly and multiply by each factor

00:18 Collect terms

00:23 We want to isolate the unknown Y

00:31 We'll arrange the equation so that Y is alone on one side

00:45 Isolate the unknown Y

00:57 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

$12y+3y-10+7(y-4)=2y$

$y=?$

Step-by-step solution

To solve the equation $12y + 3y - 10 + 7(y - 4) = 2y$ , follow these detailed steps:

Step 1: Apply the distributive property to $7(y - 4)$ .

This results in:
$12y + 3y - 10 + 7y - 28 = 2y$ .

Step 2: Combine like terms on the left side of the equation.

Combining terms, we have:
$(12y + 3y + 7y) - 10 - 28 = 2y$
$22y - 38 = 2y$ .

Step 3: Move all terms involving $y$ to one side of the equation and constant terms to the other side.

Subtract $2y$ from both sides:
$22y - 2y = 38$
$20y = 38$ .

Step 4: Solve for $y$ by dividing both sides by 20.

$y = \frac{38}{20} = 1.9$ .

Therefore, the solution to the equation is $y = 1.9$ .

Final Answer

$1.9$

Key Points to Remember

Essential concepts to master this topic

Distributive Property: Multiply term outside parentheses by every term inside
Technique: Combine like terms: 12y + 3y + 7y = 22y
Check: Substitute y = 1.9: 22(1.9) - 38 = 2(1.9) gives 3.8 = 3.8 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute to all terms in parentheses
Don't just multiply 7 × y = 7y and ignore the -4 inside parentheses = missing -28! This gives you 22y - 10 = 2y instead of 22y - 38 = 2y, leading to the wrong answer y = -0.5. Always distribute to every term inside parentheses: 7(y - 4) = 7y - 28.

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 distribute 7 to both y and -4?

The distributive property says you must multiply the outside number by every term inside the parentheses. So $7(y - 4) = 7 \times y + 7 \times (-4) = 7y - 28$ .

How do I combine like terms correctly?

Look for terms with the same variable and power. Here, combine all the y terms: $12y + 3y + 7y = 22y$ , and combine constants: $-10 + (-28) = -38$ .

What if I get a decimal answer like 1.9?

Decimal answers are perfectly valid! You can also write it as a fraction: $y = \frac{38}{20} = \frac{19}{10} = 1.9$ . Both forms are correct.

How do I move terms to isolate y?

Use inverse operations. To move $2y$ from the right side, subtract it from both sides: $22y - 2y = 38$ . This gives you $20y = 38$ .

Why do I divide by 20 at the end?

To isolate y, you need to undo the multiplication by 20. Since $20y = 38$ , divide both sides by 20: $y = \frac{38}{20} = 1.9$ .

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Solve Linear Equation: 12y+3y-10+7(y-4)=2y Step-by-Step

Linear Equations with Distributive Property

❤️ 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 distribute 7 to both y and -4?

How do I combine like terms correctly?

What if I get a decimal answer like 1.9?

How do I move terms to isolate y?

Why do I divide by 20 at the end?

🌟 Unlock Your Math Potential

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