Simplify the Expression: (-x)+(-5x) Using Like Terms

Q: Why is (-x) the same as -1x?

The coefficient of x is understood to be 1, so (-x) means negative one times x, which we write as -1x. This makes it easier to combine with other x terms.

Q: How do I know when to add or subtract the coefficients?

Look at the signs carefully! When you have (-x) + (-5x), you're adding two negative terms. Think of it as: negative 1x plus negative 5x equals negative 6x.

Q: Do I always write the answer with the negative sign first?

Yes! When the result is negative, write it as -6x, not as x(-6). The negative coefficient comes before the variable for standard form.

Adding Like Terms with Negative Signs

Simplify the following expression:

$(-x)+(-5x)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's start simplifying!

00:10 Imagine a point labeled as negative X, on our number line.

00:15 Remember, when you multiply a positive by a negative, the result is negative.

00:21 Now, let's organize the terms together for clarity.

00:25 And, that's how we find the solution to this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Simplify the following expression:

$(-x)+(-5x)=$

Step-by-step solution

Note the following rule:

$+(-x)=-x$

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

$-x-5x=$

We'll add negative $x$ to the number line and move 5 steps to the left:

Therefore, the solution is:

$-x-5x=-6x$

Final Answer

$-6x$

Key Points to Remember

Essential concepts to master this topic

Rule: When adding like terms, combine coefficients while keeping the variable
Technique: Rewrite (-x) + (-5x) as -x - 5x = -6x
Check: Count total negative x terms: one -x plus five -x equals six -x ✓

Common Mistakes

Avoid these frequent errors

Forgetting negative signs when combining terms
Don't treat (-x) + (-5x) as x + 5x = 6x! This ignores the negative signs and gives a positive result instead of negative. Always pay attention to the signs: (-x) + (-5x) means -1x + (-5x) = -6x.

Practice Quiz

Test your knowledge with interactive questions

$$ -5-(-2)= $$

FAQ

Everything you need to know about this question

Why is (-x) the same as -1x?

The coefficient of x is understood to be 1, so (-x) means negative one times x, which we write as -1x. This makes it easier to combine with other x terms.

How do I know when to add or subtract the coefficients?

Look at the signs carefully! When you have (-x) + (-5x), you're adding two negative terms. Think of it as: negative 1x plus negative 5x equals negative 6x.

Can I use a number line to help me understand this?

Absolutely! Start at -x on the number line, then move 5 more steps in the negative direction (because you're adding -5x). You'll land at -6x.

What if one term was positive instead?

If you had (-x) + (+5x), you'd get 4x because you're combining -1x + 5x. The positive term is larger, so the result is positive.

Do I always write the answer with the negative sign first?

Yes! When the result is negative, write it as -6x, not as x(-6). The negative coefficient comes before the variable for standard form.

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