Simplify the Expression: (-x)-(+3x) Using Sign Rules

Sign Rules with Algebraic Subtraction

Simplify the following expression:

(x)(+3x)= ? (-x)-(+3x)=\text{ ?}

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Step-by-step video solution

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00:00 Simply
00:03 Negative times positive is always negative
00:06 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Simplify the following expression:

(x)(+3x)= ? (-x)-(+3x)=\text{ ?}

2

Step-by-step solution

Note the following rule:

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

Now let's write the exercise in the following way:

x3x= -x-3x=

We'll add negative x x to the values on the number line and move 3 steps to the left:

-X-X-X-4X-4X-4X-3X-3X-3X-2X-2X-2X

Therefore, the solution is:

x3x=4x -x-3x=-4x

3

Final Answer

4x -4x

Key Points to Remember

Essential concepts to master this topic
  • Sign Rule: Subtracting a positive equals adding its negative
  • Technique: Rewrite (+3x) -(+3x) as 3x -3x , then combine x3x -x-3x
  • Check: Count coefficients: -1x + (-3x) = -4x ✓

Common Mistakes

Avoid these frequent errors
  • Treating subtraction as addition
    Don't change (x)(+3x) (-x)-(+3x) to x+3x=2x -x+3x = -2x ! This ignores the subtraction sign and gives the wrong answer. Always convert (+3x) -(+3x) to 3x -3x first.

Practice Quiz

Test your knowledge with interactive questions

a is negative number.

b is negative number.

What is the sum of a+b?

FAQ

Everything you need to know about this question

Why does subtracting a positive number make it negative?

+

Think of it as removing something positive, which moves you in the negative direction. The rule (+x)=x -(+x) = -x means 'the opposite of positive x is negative x'.

How do I combine x -x and 3x -3x ?

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Both terms have the same variable x, so add their coefficients: 1+(3)=4 -1 + (-3) = -4 . The result is 4x -4x .

What if I see (+x)(+3x) (+x)-(+3x) instead?

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The same rule applies! (+x)=x (+x) = x and (+3x)=3x -(+3x) = -3x , so you get x3x=2x x - 3x = -2x .

Can I use a number line for this?

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Absolutely! Start at x -x , then move 3x units to the left (subtracting). You'll land at 4x -4x on the number line.

Why is the answer negative?

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Both terms are negative: x -x and 3x -3x . When you add two negative numbers, the result is always negative and larger in magnitude.

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