Solve the Equation: Finding the Missing Number in ?:(-6)+[-2(94-73)]=-153

Q: What does the colon symbol mean in this equation?

The colon (:) represents division in this problem. So $ x:(-6) $ means $ x \div (-6) $ or $ \frac{x}{-6} $.

Q: Why do I need to solve the brackets before dealing with x?

Following order of operations (PEMDAS) is crucial! You must simplify $ [-2(94-73)] $ first to get the correct right side of the equation before solving for x.

Q: How do I handle the negative signs when multiplying?

Remember: negative times positive equals negative. So $ -2 \times 21 = -42 $. When you have $ (-6) + (-42) $, it becomes $ -6 - 42 = -48 $.

Q: Why do I multiply by -6 at the end instead of dividing?

To isolate x, you need to undo the division by -6. The opposite operation of division is multiplication, so you multiply both sides by -6 to get x alone.

Q: How can I check if x = 666 is correct?

Substitute back: $ 666 \div (-6) + (-42) = -111 + (-42) = -153 $ ✓. If both sides equal -153, your answer is right!

Division Equations with Order of Operations

Fill in the missing number:

$?\colon(-6)+\lbrack-2(94-73)\rbrack=-153$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Start with the inner parentheses

00:20 Continue to solve the parentheses

00:45 A plus sign before a minus becomes a minus

00:49 Add 42 to both sides to isolate the variable

01:14 Multiply both sides by minus 6

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Fill in the missing number:

$?\colon(-6)+\lbrack-2(94-73)\rbrack=-153$

Step-by-step solution

We begin by solving the innermost parentheses:

$94-73=21$

We obtain the following calculation:

$x\colon(-6)+\lbrack-2(21)\rbrack=-153$

Next we focus on the parentheses and multiply:

$-2\times21=-42$

We obtain the following calculation:

$x\colon(-6)+(-42)=-153$

Let's consider the multiplication between minus and plus:

$x\colon(-6)-42=-153$

We swap sections:

$x\colon(-6)=-153+42$

$x\colon(-6)=-111$

$\frac{x}{-6}=-111$

Lastly we multiply by minus 6:

$x=-111\times-6=666$

Final Answer

$x=666$

Key Points to Remember

Essential concepts to master this topic

Order: Solve parentheses first, then multiplication, then addition/subtraction
Technique: Work step by step: 94-73=21, then -2×21=-42
Check: Substitute x=666: 666÷(-6)+(-42)=-111-42=-153 ✓

Common Mistakes

Avoid these frequent errors

Ignoring order of operations when simplifying
Don't solve x÷(-6)+[-2(94-73)]=-153 by working left to right randomly = wrong simplification! This ignores PEMDAS and creates calculation errors. Always follow order of operations: parentheses first, then multiplication, then division and addition.

Practice Quiz

Test your knowledge with interactive questions

$$ 11=a-16 $$

$a=\text{?}$

FAQ

Everything you need to know about this question

What does the colon symbol mean in this equation?

The colon (:) represents division in this problem. So $x:(-6)$ means $x \div (-6)$ or $\frac{x}{-6}$ .

Why do I need to solve the brackets before dealing with x?

Following order of operations (PEMDAS) is crucial! You must simplify $[-2(94-73)]$ first to get the correct right side of the equation before solving for x.

How do I handle the negative signs when multiplying?

Remember: negative times positive equals negative. So $-2 \times 21 = -42$ . When you have $(-6) + (-42)$ , it becomes $-6 - 42 = -48$ .

Why do I multiply by -6 at the end instead of dividing?

To isolate x, you need to undo the division by -6. The opposite operation of division is multiplication, so you multiply both sides by -6 to get x alone.

How can I check if x = 666 is correct?

Substitute back: $666 \div (-6) + (-42) = -111 + (-42) = -153$ ✓. If both sides equal -153, your answer is right!

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Solve the Equation: Finding the Missing Number in ?:(-6)+[-2(94-73)]=-153

Division Equations with Order of Operations

❤️ 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

What does the colon symbol mean in this equation?

Why do I need to solve the brackets before dealing with x?

How do I handle the negative signs when multiplying?

Why do I multiply by -6 at the end instead of dividing?

How can I check if x = 666 is correct?

🌟 Unlock Your Math Potential

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