Solve Linear Expression: Expanding 2x + 5(x-5)

Q: Why do I multiply 5 by both x and -5?

The distributive property says you must multiply the outside number by every term inside the parentheses. So $ 5(x-5) $ becomes $ 5 \times x + 5 \times (-5) = 5x - 25 $.

Q: How do I know which terms are like terms?

Like terms have the same variable with the same exponent. Here, $ 2x $ and $ 5x $ are like terms because both have variable x to the first power, so $ 2x + 5x = 7x $.

Q: What if I get confused by the negative sign?

Think of it as $ 5(x + (-5)) $. When you distribute: $ 5 \times x = 5x $ and $ 5 \times (-5) = -25 $. The negative stays with the 25!

Q: Can I solve this problem in a different order?

You should always follow the order of operations! First handle what's in parentheses by using the distributive property, then combine like terms. Don't try to add $ 2x + 5 $ first.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve the problem together!

00:08 First, open the parentheses carefully. Multiply each factor one by one.

00:13 Write each multiplication separately to keep it clear.

00:19 Remember, always solve multiplication and division before you handle addition and subtraction.

00:31 Continue solving in order, from left to right.

00:34 And there you have it! That's the solution to the problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$2x+5(x-5)=$

2

Step-by-step solution

We simplify the exercise in parentheses as follows:

$2x+(5\times x)-(5\times5)=$

We solve the exercises in parentheses:

$2x+5x-25=$

We add like terms:

$2x+5x=7x$

We obtain

$7x-25$

3

Final Answer

$7x-25$

Key Points to Remember

Essential concepts to master this topic

Distributive Property: Multiply each term inside parentheses by outside factor
Technique: $5(x-5) = 5x - 25$ by distributing the 5
Check: Combine like terms $2x + 5x = 7x$ to get final answer ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute the negative sign
Don't just multiply 5 × x = 5x and forget the second term! This gives 2x + 5x = 7x instead of the correct 7x - 25. Always distribute to every term inside the parentheses: 5(x - 5) = 5x - 25.

Practice Quiz

Test your knowledge with interactive questions

$$ 94+12+6= $$

FAQ

Everything you need to know about this question

Why do I multiply 5 by both x and -5?

+

The distributive property says you must multiply the outside number by every term inside the parentheses. So $5(x-5)$ becomes $5 \times x + 5 \times (-5) = 5x - 25$ .

How do I know which terms are like terms?

+

Like terms have the same variable with the same exponent. Here, $2x$ and $5x$ are like terms because both have variable x to the first power, so $2x + 5x = 7x$ .

What if I get confused by the negative sign?

+

Think of it as $5(x + (-5))$ . When you distribute: $5 \times x = 5x$ and $5 \times (-5) = -25$ . The negative stays with the 25!

Can I solve this problem in a different order?

+

You should always follow the order of operations! First handle what's in parentheses by using the distributive property, then combine like terms. Don't try to add $2x + 5$ first.

How do I check if my final answer is correct?

+

You can't substitute a value since this isn't an equation to solve - it's an expression to simplify. Instead, pick any number for x (like x = 1) and check that both $2x + 5(x-5)$ and $7x - 25$ give the same result.

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Solve Linear Expression: Expanding 2x + 5(x-5)

Distributive Property with Negative Constants

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