Solve 23-12×(-6)+?÷7=102: Order of Operations Challenge

Q: Why does negative times negative equal positive?

Think of it as opposite of opposite. When you multiply by a negative, you flip direction. Flipping twice gets you back to positive! So $ -12 \times (-6) = +72 $.

Q: What's the difference between : and ÷ symbols?

They mean exactly the same thing - division! The colon (:) is just another way to write division, commonly used in some countries. So $ x:7 = x÷7 = \frac{x}{7} $.

Q: How do I handle the subtraction of a negative number?

Remember: subtracting a negative is the same as adding a positive! So $ 23 - (-72) = 23 + 72 = 95 $.

Q: Should I solve for x step by step or all at once?

Step by step is much safer! First simplify the left side using order of operations, then isolate the term with x, finally solve for x.

Q: What if I get a different answer when checking?

Go back and check your order of operations first! Most errors happen from multiplying in wrong order or handling negative signs incorrectly.

Order of Operations with Negative Numbers

What is the missing number?

$23-12\times(-6)+\red{\boxed{?}}\colon7=102$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve the expression according to the order of operations wherever possible

00:20 Two minuses = plus

00:37 Subtract 95 from both sides in order to isolate X

00:47 Multiply both sides by 7 - we want to know what X equals

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the missing number?

$23-12\times(-6)+\red{\boxed{?}}\colon7=102$

Step-by-step solution

First, we solve the multiplication exercise:

$12\times(-6)=-72$

Now we get:

$23-(-72)+x\colon7=102$

Let's pay attention to the minus signs, remember that a negative times a negative equals a positive.

We multiply them one by one to be able to open the parentheses:

$23+72+x\colon7=102$

We reduce:

$95+x:7=102$

We move the sections:

$x:7=102-95$

$x:7=7$

$\frac{x}{7}=7$

Multiply by 7:

$x=7\times7=49$

Final Answer

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Multiply first, then add/subtract from left to right
Technique: Negative times negative equals positive: $-12 \times (-6) = +72$
Check: Substitute x = 49 back into original equation to verify ✓

Common Mistakes

Avoid these frequent errors

Ignoring order of operations and solving left to right
Don't solve 23-12 first then multiply by (-6) = wrong answer of -66! This violates PEMDAS and creates massive errors. Always multiply and divide first, then add and subtract.

Practice Quiz

Test your knowledge with interactive questions

$$ 100+5-100+5 $$

FAQ

Everything you need to know about this question

Why does negative times negative equal positive?

Think of it as opposite of opposite. When you multiply by a negative, you flip direction. Flipping twice gets you back to positive! So $-12 \times (-6) = +72$ .

What's the difference between : and ÷ symbols?

They mean exactly the same thing - division! The colon (:) is just another way to write division, commonly used in some countries. So $x:7 = x÷7 = \frac{x}{7}$ .

How do I handle the subtraction of a negative number?

Remember: subtracting a negative is the same as adding a positive! So $23 - (-72) = 23 + 72 = 95$ .

Should I solve for x step by step or all at once?

Step by step is much safer! First simplify the left side using order of operations, then isolate the term with x, finally solve for x.

What if I get a different answer when checking?

Go back and check your order of operations first! Most errors happen from multiplying in wrong order or handling negative signs incorrectly.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Linear Equations (One Variable) questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

Solve 23-12×(-6)+?÷7=102: Order of Operations Challenge

Order of Operations with Negative Numbers

❤️ 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 does negative times negative equal positive?

What's the difference between : and ÷ symbols?

How do I handle the subtraction of a negative number?

Should I solve for x step by step or all at once?

What if I get a different answer when checking?

🌟 Unlock Your Math Potential

More Questions

Solving Equations by using Addition/ Subtraction

Solve for X: (10x-1/5)·1/2 = -1/10+8x Linear Equation

Solve for X: Finding Camila's Balls When Total is 16 and Difference is 8

Solve for X: 16(1/4x-2) = 3x+1/2 Linear Equation

Solve for X: Finding X in (1/4)(x-16) + (3/4)x = 8x-11

All Operations in the Order of Operations

Solve the Expression: 20-(1+9:9) Using Order of Operations

Compare Expressions: 14+16:4×2 vs 14+16:(4×2) - Order of Operations

Solve 19×(20-4×5): Order of Operations Practice

Solve Division Problem: 225÷[(26-6÷3)×5] Using Order of Operations

Addition, Subtraction, Multiplication and Division

Compare Expressions: 24:6:2 vs 24:(6:2) - Which Sign Fits?

Compare Expressions: Finding the Sign Between 4+7-3+1-5 and 4+(7-3+1-5)

Solve 8:2(2+2): Order of Operations Challenge

Solve Division Expression: 12÷(4×2-9÷3) Step-by-Step Solution

Solving an Equation by Multiplication/ Division

Solve the Linear Equation: Finding X in 5x = 3

Solve for X in the Linear Equation 3x = 18

Triangle ABC: Solving for Angle C When A+B=2C and B=3A

Solve the Linear Equation: Finding X in 5x-8=10x+22