Solve (-x)-(-6x): Simplifying Expressions with Negative Terms

Q: Why does subtracting a negative become addition?

Think of it as owing a debt. If someone takes away your debt of $6, you actually gain $6! Similarly, $ -(-6x) $ means "take away negative 6x" which gives you positive 6x.

Q: How do I remember the double negative rule?

Use the phrase "two negatives make a positive". Just like in language: "I don't have no money" actually means "I have money." In math: $ -(-x) = +x $

Q: Can I work left to right without rewriting?

Yes, but be extra careful! $ (-x) - (-6x) $ becomes $ -x + 6x $ in one step. Just remember: subtracting negative = adding positive.

Algebraic Expressions with Double Negatives

Solve the following expression:

$(-x)-(-6x)=\text{ ?}$

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Step-by-step video solution

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00:00 Simply

00:02 Negative times negative always equals positive

00:05 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

Solve the following expression:

$(-x)-(-6x)=\text{ ?}$

Step-by-step solution

Note the following rule:

$-(-x)=+x$

Now let's rewrite the exercise as follows:

$-x+6x=$

Then, we will write -x on the number line and move 6 steps to the right:

Therefore, the solution is:

$-x+6x=5x$

Final Answer

$5x$

Key Points to Remember

Essential concepts to master this topic

Rule: Double negative becomes positive: -(-6x) = +6x
Technique: Rewrite (-x) - (-6x) as -x + 6x = 5x
Check: Substitute x = 2: (-2) - (-12) = -2 + 12 = 10 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to change the sign when removing double negatives
Don't write -(-6x) = -6x! This ignores the negative-negative rule and gives -7x instead of 5x. Always remember that subtracting a negative means adding the positive: -(-6x) = +6x.

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 negative become addition?

Think of it as owing a debt. If someone takes away your debt of $6, you actually gain$ 6! Similarly, $-(-6x)$ means "take away negative 6x" which gives you positive 6x.

How do I remember the double negative rule?

Use the phrase "two negatives make a positive". Just like in language: "I don't have no money" actually means "I have money." In math: $-(-x) = +x$

What's the difference between -x and (-x)?

They're the same thing! The parentheses in (-x) just help clarify that we're talking about negative x as a whole term. Both represent the opposite of x.

Can I work left to right without rewriting?

Yes, but be extra careful! $(-x) - (-6x)$ becomes $-x + 6x$ in one step. Just remember: subtracting negative = adding positive.

How do I check my answer?

Pick any value for x (like x = 1) and substitute into both the original expression and your answer. If $(-1) - (-6) = 5$ and $5(1) = 5$ , you're correct!

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