Solve (-x)+(+2x): Combining Like Terms with Opposite Signs

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

When a variable has no visible coefficient, it actually has a coefficient of 1. So x = 1x and -x = -1x. This makes combining like terms much clearer!

Q: How do I add -1 and +2?

Use the number line method! Start at -1, then move 2 spaces to the right (because +2 is positive). You'll land on +1, so $ -1 + 2 = 1 $.

Q: What if I got -3x instead of x?

You might have subtracted instead of adding coefficients. Remember: $ (-x) + (+2x) $ means addition, so calculate $ -1 + 2 = 1 $, not $ -1 - 2 = -3 $.

Q: Can I write the answer as 1x?

Yes, $ 1x $ is mathematically correct! However, we usually simplify by writing just $ x $ since the coefficient 1 is understood.

Q: How do I check my work?

Pick any number for x and substitute it into both the original expression and your answer. If x = 5: $ (-5) + (+10) = 5 $ and your answer gives 5. They match! ✓

Combining Like Terms with Negative Coefficients

$(-x)+(+2x)=$

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Step-by-step video solution

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00:00 Simply

00:05 Let's arrange the equation so it will be easy to solve

00:09 And this is the solution to the question

Step-by-step written solution

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Understand the problem

$(-x)+(+2x)=$

Step-by-step solution

To solve this problem, follow these steps:

Step 1: Identify and combine the like terms in the expression $(-x) + (+2x)$ .
Step 2: Focus on the coefficients of $x$ . The term $-x$ can be seen as $-1x$ , and the term $+2x$ has a coefficient of $+2$ .
Step 3: Add the coefficients of these like terms: $-1 + 2 = 1$ .

Now, let's simplify:

Starting with the expression:
$(-x) + (+2x) = -1x + 2x$ .
Combine the coefficients: $(-1 + 2)x = 1x$ .

This simplifies to $x$ , as $1x$ is simply $x$ .

Therefore, the solution to the problem is $x$ .

Final Answer

$x$

Key Points to Remember

Essential concepts to master this topic

Rule: Combine like terms by adding their coefficients together
Technique: Write -x as -1x, then add: -1 + 2 = 1
Check: Substitute any value: if x = 3, then -3 + 6 = 3 ✓

Common Mistakes

Avoid these frequent errors

Treating signs and coefficients separately
Don't think of -x and +2x as separate sign and number parts = confusing errors! This leads to wrong operations like subtracting instead of adding coefficients. Always identify the complete coefficient including its sign: -1 and +2.

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 is -x the same as -1x?

When a variable has no visible coefficient, it actually has a coefficient of 1. So x = 1x and -x = -1x. This makes combining like terms much clearer!

How do I add -1 and +2?

Use the number line method! Start at -1, then move 2 spaces to the right (because +2 is positive). You'll land on +1, so $-1 + 2 = 1$ .

What if I got -3x instead of x?

You might have subtracted instead of adding coefficients. Remember: $(-x) + (+2x)$ means addition, so calculate $-1 + 2 = 1$ , not $-1 - 2 = -3$ .

Can I write the answer as 1x?

Yes, $1x$ is mathematically correct! However, we usually simplify by writing just $x$ since the coefficient 1 is understood.

How do I check my work?

Pick any number for x and substitute it into both the original expression and your answer. If x = 5: $(-5) + (+10) = 5$ and your answer gives 5. They match! ✓

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