Solve the Expression: Adding Like Terms in (+x)+(+3x)

Q: Why are there parentheses around the positive signs?

The parentheses are just for emphasis to show the signs clearly. $ (+x) = x $ and $ (+3x) = 3x $. They don't change the values at all!

Q: How do I know when terms are 'like terms'?

Like terms have the exact same variable part. Since both x and 3x contain just the variable x, they're like terms and can be combined.

Q: What if I had different variables like x and y?

You cannot combine different variables! For example, $ x + 3y $ stays as $ x + 3y $ because x and y are unlike terms.

Q: Is there a faster way to add like terms?

Yes! Just add the coefficients (the numbers in front): 1x + 3x means 1 + 3 = 4, so the answer is 4x.

Q: What happens if there's no number in front of x?

When you see just x, there's an invisible coefficient of 1. So x really means 1x, making it easy to add with other terms.

Adding Like Terms with Positive Signs

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 First, let's simplify things.

00:10 Find the point X on the axis.

00:13 Add three X to the positive side of the axis.

00:18 Now, collect the like terms.

00:20 And that's how we solve the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

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

Step-by-step solution

First let's remember the rule:

$+(+x)=+x$

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

$x+3x=$

We'll can then add $x$ to the number line values and move 3 steps to the right:

Therefore, the solution is:

$x+3x=4x$

Final Answer

$4x$

Key Points to Remember

Essential concepts to master this topic

Rule: When adding like terms, combine the coefficients
Technique: Simplify (+x) to x, then add: x + 3x = 4x
Check: If x = 2, then 4x = 8 equals 2 + 6 ✓

Common Mistakes

Avoid these frequent errors

Getting confused by the positive signs
Don't think (+x) + (+3x) becomes negative or subtract = wrong answer like -4x or 2x! The parentheses around positive signs don't change the values. Always remember that (+x) simply equals x and add normally.

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 are there parentheses around the positive signs?

The parentheses are just for emphasis to show the signs clearly. $(+x) = x$ and $(+3x) = 3x$ . They don't change the values at all!

How do I know when terms are 'like terms'?

Like terms have the exact same variable part. Since both x and 3x contain just the variable x, they're like terms and can be combined.

What if I had different variables like x and y?

You cannot combine different variables! For example, $x + 3y$ stays as $x + 3y$ because x and y are unlike terms.

Is there a faster way to add like terms?

Yes! Just add the coefficients (the numbers in front): 1x + 3x means 1 + 3 = 4, so the answer is 4x.

What happens if there's no number in front of x?

When you see just x, there's an invisible coefficient of 1. So x really means 1x, making it easy to add with other terms.

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