Simplifying Linear Expressions Involving Variables: 12x-(24x+35y)-(93x-48y)

Q: How do I keep track of all the signs when distributing?

Write each step clearly! First distribute: $ 12x-24x-35y-93x+48y $. Then group like terms: $ (12x-24x-93x)+(-35y+48y) $.

Q: What's the difference between combining like terms and distributing?

Distributing removes parentheses by multiplying. Combining like terms adds or subtracts terms with the same variable. You must distribute first, then combine!

Q: Can I rearrange terms before combining them?

Yes! You can rearrange terms to group like terms together: $ 12x-24x-93x-35y+48y $. This makes combining easier and reduces errors.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Negative times positive is always negative

00:21 Negative times negative is always positive

00:29 Collect like terms

00:39 We'll use the commutative law to arrange the exercise

00:52 We'll solve one operation at a time

01:03 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$12x-(24x+35y)-(93x-48y)=\text{?}$

2

Step-by-step solution

To solve this expression, let's proceed step-by-step:

Step 1: Apply the Distributive Property to remove the parentheses:
The original expression is $12x - (24x + 35y) - (93x - 48y)$ .
Distribute the negative signs:
$= 12x - 24x - 35y - 93x + 48y$ .
Step 2: Combine like terms:
For $x$ -terms: Combine $12x - 24x - 93x$ :
$12x - 24x = -12x$
$-12x - 93x = -105x$ .
For $y$ -terms: Combine $-35y + 48y$ :
$-35y + 48y = 13y$ .
Step 3: Put the combined terms together:
Therefore, the simplified expression is $13y - 105x$ .

The solution to the expression is $13y - 105x$ .

3

Final Answer

$13y-105x$

Key Points to Remember

Essential concepts to master this topic

Distribution Rule: Apply negative signs to each term inside parentheses
Technique: Change signs carefully: -(24x+35y) becomes -24x-35y
Check: Combine like terms systematically: x-terms first, then y-terms ✓

Common Mistakes

Avoid these frequent errors

Incorrect sign distribution when removing parentheses
Don't forget to change signs when distributing negatives = wrong coefficients! Students often write -(93x-48y) as -93x-48y instead of -93x+48y. Always flip every sign inside parentheses when there's a negative outside.

Practice Quiz

Test your knowledge with interactive questions

$70:(14\times5)=$

FAQ

Everything you need to know about this question

Why does -(93x-48y) become -93x+48y instead of -93x-48y?

+

The negative sign outside parentheses acts like multiplying by -1. So -(93x-48y) = -1(93x-48y) = -93x+48y. The negative of a negative becomes positive!

How do I keep track of all the signs when distributing?

+

Write each step clearly! First distribute: $12x-24x-35y-93x+48y$ . Then group like terms: $(12x-24x-93x)+(-35y+48y)$ .

What's the difference between combining like terms and distributing?

+

Distributing removes parentheses by multiplying. Combining like terms adds or subtracts terms with the same variable. You must distribute first, then combine!

Can I rearrange terms before combining them?

+

Yes! You can rearrange terms to group like terms together: $12x-24x-93x-35y+48y$ . This makes combining easier and reduces errors.

How do I check if my final answer is correct?

+

Substitute simple values like x=1, y=1 into both the original expression and your answer. If they give the same result, your simplification is correct! Always verify your work.

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Simplifying Linear Expressions Involving Variables: 12x-(24x+35y)-(93x-48y)

Distributive Property with Multiple Parentheses

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