Solve for x: Breaking Down the Equation 84/(2*7) - (63 - 2x) = ?

Q: Why do I calculate 84 ÷ (2 × 7) first?

Follow the order of operations (PEMDAS)! Operations inside parentheses come first: 2 × 7 = 14, then division: $ 84 ÷ 14 = 6 $.

Q: How do I handle the minus sign before (63 - 2x)?

The minus sign distributes to every term inside the parentheses. So $ -(63 - 2x) = -63 + 2x $. Think of it as $ -1 × (63 - 2x) $.

Q: Can I rearrange 2x - 57 to -57 + 2x?

Yes! Both forms are mathematically equivalent due to the commutative property. However, $ 2x - 57 $ is the standard form with the variable term first.

Q: What if I forgot the order of operations?

Use PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Always do operations inside parentheses first!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Let's write division as a fraction

00:06 Negative times positive always equals negative

00:09 Negative times negative always equals positive

00:16 Let's factor 82 into factors 42 and 2

00:20 Let's reduce what we can

00:25 Let's factor 42 into factors 7 and 6

00:32 Let's reduce what we can

00:44 Let's use the distribution law and split 63 into 60 and 3

00:58 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

$84:(2\cdot7)-(63-2x)=\text{?}$

2

Step-by-step solution

To solve the expression $84:(2\cdot7)-(63-2x)$ , we shall simplify step-by-step as follows:

Firstly, simplify the division: $84 \div (2 \cdot 7)$ .
- Calculate $2 \cdot 7 = 14$ .
- Then, perform the division: $84 \div 14 = 6$ .
Now, substitute the value from the division back into the main expression: $6 - (63 - 2x)$ .
Simplify the expression inside the parentheses: $63 - 2x$ .
Finally, apply the subtraction:
- Distribute the negative sign: $6 - 63 + 2x$ .
- Combine the constant terms: $-57 + 2x$ .

Therefore, the expression simplifies to $2x - 57$ .

3

Final Answer

$2x-57$

Key Points to Remember

Essential concepts to master this topic

Order of Operations: Calculate division first, then handle parentheses
Distribution: When subtracting (63 - 2x), change signs to get -63 + 2x
Check: Substitute a test value to verify 2x - 57 is correct ✓

Common Mistakes

Avoid these frequent errors

Incorrectly distributing the negative sign
Don't just remove parentheses without changing signs: 6 - (63 - 2x) ≠ 6 - 63 - 2x! This keeps the wrong sign on 2x and gives -2x - 57. Always distribute the negative: 6 - (63 - 2x) = 6 - 63 + 2x.

Practice Quiz

Test your knowledge with interactive questions

$$ 100-(30-21)= $$

FAQ

Everything you need to know about this question

Why do I calculate 84 ÷ (2 × 7) first?

+

Follow the order of operations (PEMDAS)! Operations inside parentheses come first: 2 × 7 = 14, then division: $84 ÷ 14 = 6$ .

How do I handle the minus sign before (63 - 2x)?

+

The minus sign distributes to every term inside the parentheses. So $-(63 - 2x) = -63 + 2x$ . Think of it as $-1 × (63 - 2x)$ .

Can I rearrange 2x - 57 to -57 + 2x?

+

Yes! Both forms are mathematically equivalent due to the commutative property. However, $2x - 57$ is the standard form with the variable term first.

What if I forgot the order of operations?

+

Use PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Always do operations inside parentheses first!

How can I check if my final answer is right?

+

Pick any value for x (like x = 10) and substitute it into both the original expression and your answer. If you get the same result from both, your simplification is correct! $2(10) - 57 = -37$ .

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Solve for x: Breaking Down the Equation 84/(2*7) - (63 - 2x) = ?

Algebraic Simplification with Distribution

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