Solve the Linear Equation: 3(y-2)+2(y+3)=180

Q: What does 'distribute' mean in math?

Distributing means multiplying the number outside the parentheses by each term inside. For example: $ 3(y-2) = 3 \times y + 3 \times (-2) = 3y - 6 $

Q: Why do we combine like terms?

Like terms have the same variable (like 3y and 2y). Combining them simplifies the equation: $ 3y + 2y = 5y $, making it easier to solve!

Q: What if the constants don't cancel out like -6 + 6?

That's totally normal! Sometimes you'll get something like $ 5y + 4 = 180 $. Just subtract 4 from both sides to isolate the variable term.

Q: How do I know which terms are 'like terms'?

Like terms: 3y and 2y (both have y)Like terms: -6 and +6 (both are constants)Unlike terms: 3y and -6 (variable vs constant)

Linear Equations with Distribution and Combining

$3(y-2)+2(y+3)=180$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Open parentheses properly, multiply by each factor

00:14 Collect terms

00:23 Isolate Y

00:34 Break the fraction into two integers and then combine

00:37 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

$3(y-2)+2(y+3)=180$

Step-by-step solution

To solve this equation, we follow these steps:

Step 1: Distribute the coefficients within the parentheses.
Step 2: Combine like terms.
Step 3: Rearrange the equation to isolate and solve for $y$ .

Let's apply these steps to solve the equation $3(y-2)+2(y+3)=180$ :

Step 1: Distribute the terms:
$3(y-2) + 2(y+3) = 3y - 6 + 2y + 6$ .

Step 2: Combine like terms:
Combine the $y$ terms and the constant terms: $3y + 2y - 6 + 6 = 5y$ .
Thus, the equation simplifies to $5y = 180$ .

Step 3: Solve for $y$ :
To find $y$ , divide both sides by 5:
$5y / 5 = 180 / 5$ , which simplifies to $y = 36$ .

Therefore, the solution to the equation is $y = 36$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Distribution Rule: Apply coefficient to each term inside parentheses
Technique: Combine like terms: 3y + 2y = 5y, -6 + 6 = 0
Check: Substitute y = 36: 3(36-2) + 2(36+3) = 102 + 78 = 180 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute to all terms inside parentheses
Don't just multiply 3 × y and ignore the -2, getting 3y - 2 instead of 3y - 6! This gives completely wrong coefficients. Always distribute the outside number to every single term inside the parentheses.

Practice Quiz

Test your knowledge with interactive questions

$$ 5x=1 $$

What is the value of x?

FAQ

Everything you need to know about this question

What does 'distribute' mean in math?

Distributing means multiplying the number outside the parentheses by each term inside. For example: $3(y-2) = 3 \times y + 3 \times (-2) = 3y - 6$

Why do we combine like terms?

Like terms have the same variable (like 3y and 2y). Combining them simplifies the equation: $3y + 2y = 5y$ , making it easier to solve!

What if the constants don't cancel out like -6 + 6?

That's totally normal! Sometimes you'll get something like $5y + 4 = 180$ . Just subtract 4 from both sides to isolate the variable term.

Can I solve this without distributing first?

It's much harder! You could try dividing both sides by something, but distributing first is the standard method because it clearly shows all terms.

How do I know which terms are 'like terms'?

Like terms: 3y and 2y (both have y)
Like terms: -6 and +6 (both are constants)
Unlike terms: 3y and -6 (variable vs constant)

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