Solve Step-by-Step: 15+5-(-4)+(-9)+8-4 Using Order of Operations

Integer Operations with Negative Numbers

Solve the following problem using the order of operations:

15+5(4)+(9)+84= 15+5-(-4)+(-9)+8-4=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:04 Calculate one operation at a time from left to right
00:09 Negative multiplied by negative always equals positive
00:30 Calculate one operation at a time from left to right
00:57 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

Solve the following problem using the order of operations:

15+5(4)+(9)+84= 15+5-(-4)+(-9)+8-4=

2

Step-by-step solution

Let's remember the rule:

(x)=+x -(-x)=+x

We'll write the exercise in the appropriate form:

15+5+4+(9)+84= 15+5+4+(-9)+8-4=

Let's solve the exercise from left to right:

15+5=20 15+5=20

Now we'll obtain the exercise:

20+4+(9)+84= 20+4+(-9)+8-4=

Let's solve the exercise from left to right:

20+4=24 20+4=24

Now we'll obtain the exercise:

24+(9)+84= 24+(-9)+8-4=

Let's remember the rule:

+(x)=x +(-x)=-x

We'll write the exercise in the appropriate form:

249+84= 24-9+8-4=

Let's solve the exercise from left to right:

249=15 24-9=15

15+8=23 15+8=23

234=19 23-4=19

3

Final Answer

19 19

Key Points to Remember

Essential concepts to master this topic
  • Rule: Double negatives become positive: (x)=+x -(-x) = +x
  • Technique: Convert (4) -(-4) to +4 +4 and +(9) +(-9) to 9 -9
  • Check: Work left to right: 15+5+4-9+8-4 = 19 ✓

Common Mistakes

Avoid these frequent errors
  • Ignoring negative sign rules
    Don't treat -(-4) as -4 = wrong answer 11! This ignores the double negative rule. Always convert -(-x) to +x first, so -(-4) becomes +4.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

\( (-2)\cdot(-4)= \)

FAQ

Everything you need to know about this question

Why does -(-4) become +4?

+

The rule is "negative of a negative equals positive". Think of it as: if you owe someone $4 (that's -4), but then they cancel that debt, you gain +4!

What's the difference between +(-9) and -(-9)?

+

+(-9) means "add negative 9" which equals -9. But -(-9) means "subtract negative 9" which equals +9. The first operation matters!

Do I solve from left to right or follow PEMDAS?

+

For addition and subtraction only, work left to right after handling negative signs. PEMDAS applies when you have parentheses, multiplication, or division mixed in.

How can I avoid sign errors?

+

First, rewrite the expression by converting all negative signs: -(-4) becomes +4, +(-9) becomes -9. Then you have: 15+5+49+84 15+5+4-9+8-4

What if I get a different answer?

+

Double-check your sign conversions first! Most errors happen when handling -(-x) or +(-x). Then work left to right carefully: 20+4-9+8-4 step by step.

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