Solve: Combining Like Terms in (+3x) + (-3x)

Q: Why does 3x + (-3x) equal 0 instead of 6x?

Because you're adding a negative, not multiplying! $ (+3x) + (-3x) $ means 3x plus negative 3x, which is the same as $ 3x - 3x = 0 $.

Q: What does it mean when like terms cancel out completely?

When like terms have opposite coefficients (like +3 and -3), they neutralize each other completely. It's like having 3 apples and taking away 3 apples - you're left with zero apples!

Q: How can I visualize this on a number line?

Start at 0, move 3 steps right for +3x, then move 3 steps left for -3x. You end up back at 0! The movements cancel each other out perfectly.

Q: What if the coefficients were different, like 5x and -3x?

Then they wouldn't cancel completely! $ 5x + (-3x) = 5x - 3x = 2x $. Only when coefficients are exactly opposite do you get zero.

Like Terms with Opposite Signs

$(+3x)+(-3x)=\text{ ?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simply

00:03 Let's take 3X in the positive direction on the axis

00:07 Now subtract 3X in the negative direction on the axis

00:12 And that's the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$(+3x)+(-3x)=\text{ ?}$

Step-by-step solution

Firstly, we will draw a number line and label 3 $x$ on it.

Since we have -3 $x$ in parentheses, we need to move 3 steps to the left on the number line:

Remember the rule:

$+(-x)=-$

Therefore, we can write the exercise as follows:

$3x-3x=0$

Final Answer

$0$

Key Points to Remember

Essential concepts to master this topic

Rule: Like terms with opposite signs cancel to zero
Technique: $(+3x) + (-3x) = 3x - 3x = 0$
Check: Opposite coefficients (3 and -3) always sum to zero ✓

Common Mistakes

Avoid these frequent errors

Adding coefficients instead of combining properly
Don't add 3 + (-3) = 0 and keep the x to get 0x! This misses that 0x equals zero, not 0x. Always remember that when like terms cancel completely, the result is simply 0.

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 3x + (-3x) equal 0 instead of 6x?

Because you're adding a negative, not multiplying! $(+3x) + (-3x)$ means 3x plus negative 3x, which is the same as $3x - 3x = 0$ .

What does it mean when like terms cancel out completely?

When like terms have opposite coefficients (like +3 and -3), they neutralize each other completely. It's like having 3 apples and taking away 3 apples - you're left with zero apples!

Is the answer 0 or 0x?

The answer is simply 0! When the coefficient becomes zero, we don't write 0x because 0 times anything equals 0. So $0x = 0$ .

How can I visualize this on a number line?

Start at 0, move 3 steps right for +3x, then move 3 steps left for -3x. You end up back at 0! The movements cancel each other out perfectly.

What if the coefficients were different, like 5x and -3x?

Then they wouldn't cancel completely! $5x + (-3x) = 5x - 3x = 2x$ . Only when coefficients are exactly opposite do you get zero.

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