Solve (+x)-(+4x): Combining Like Terms with Positive Coefficients

Q: Why does (+x)-(+4x) become x-4x?

The parentheses with plus signs don't change anything - (+x) is just x and (+4x) is just 4x. So (+x)-(+4x) simplifies to x-4x.

Q: How do I subtract like terms with the same variable?

Just subtract the coefficients (the numbers in front). For x-4x, think: 1x - 4x = -3x. The variable x stays the same.

Q: What if I had 4x - x instead?

Then you'd get +3x! The order matters: x - 4x = -3x4x - x = +3x

Q: Can I use a number line to check this?

Yes! Start at position x, then move 4 steps left (because you're subtracting 4x). You'll end up at -3x on the number line.

Like Terms with Positive and Negative Coefficients

$(+x)-(+4x)=\text{ ?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simplify

00:04 Negative times positive is always negative

00:15 Grouping factors

00:18 The coefficient of any number is always 1

00:21 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$(+x)-(+4x)=\text{ ?}$

Step-by-step solution

First, let's remember the rule:

$-(+x)=-x$

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

$x-4x=$

We'll add $x$ to the number line and go 4 steps to the left:

Therefore the solution is:

$x-4x=-3x$

Final Answer

$-3x$

Key Points to Remember

Essential concepts to master this topic

Rule: Subtracting a positive term changes it to negative
Technique: Rewrite (+x)-(+4x) as x-4x to simplify
Check: Substitute x=1: 1-4(1) = -3 matches -3x ✓

Common Mistakes

Avoid these frequent errors

Adding coefficients instead of subtracting
Don't add x + 4x = 5x when you see subtraction! This ignores the minus sign and gives the wrong result. Always pay attention to the operation: x - 4x = -3x.

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 (+x)-(+4x) become x-4x?

The parentheses with plus signs don't change anything - (+x) is just x and (+4x) is just 4x. So (+x)-(+4x) simplifies to x-4x.

How do I subtract like terms with the same variable?

Just subtract the coefficients (the numbers in front). For x-4x, think: 1x - 4x = -3x. The variable x stays the same.

Why is the answer negative?

You're starting with 1x and taking away 4x. Since you're taking away more than you started with, the result must be negative: -3x.

What if I had 4x - x instead?

Then you'd get +3x! The order matters:

x - 4x = -3x
4x - x = +3x

Can I use a number line to check this?

Yes! Start at position x, then move 4 steps left (because you're subtracting 4x). You'll end up at -3x on the number line.

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