Simplify the Expression: 7x-(4b+3x) Step by Step

Distributive Property with Negative Signs

7x(4b+3x)=? 7x-(4b+3x)=\text{?}

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Note, when multiplying negative by positive, the result is always negative:
00:14 Let's group the factors
00:19 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

7x(4b+3x)=? 7x-(4b+3x)=\text{?}

2

Step-by-step solution

First, we open the parentheses and change the sign accordingly.

Since there are only positive numbers inside the parentheses, multiplying by minus will give us negative numbers:

7x4b3x= 7x-4b-3x=

Now we group the X factors:

7x3x=4x 7x-3x=4x

Now we obtain:

4x4b 4x-4b

3

Final Answer

4x4b 4x-4b

Key Points to Remember

Essential concepts to master this topic
  • Distribution Rule: Multiply the negative sign by each term inside parentheses
  • Sign Change: 7x-(4b+3x) becomes 7x-4b-3x after distribution
  • Check: Combine like terms: 7x-3x=4x, final answer is 4x-4b ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to change signs when distributing negative
    Don't keep the same signs inside parentheses after distributing the negative = 7x-4b+3x = 10x-4b (wrong)! The negative sign must multiply each term, changing all signs. Always change +4b to -4b and +3x to -3x when distributing the minus sign.

Practice Quiz

Test your knowledge with interactive questions

\( 100-(5+55)= \)

FAQ

Everything you need to know about this question

Why does the minus sign change both terms inside the parentheses?

+

The minus sign acts like multiplying by -1. Just like (-1)×(4b+3x) = -4b-3x, the distributive property requires you to multiply each term by the negative.

What if there were already negative signs inside the parentheses?

+

Then you'd get positive results! For example: 7x-(-4b-3x) = 7x+4b+3x. Remember: negative times negative equals positive.

How do I know which terms are 'like terms' that can be combined?

+

Like terms have the same variable and exponent. In this problem, 7x and 3x are like terms because they both have 'x'. The term 4b is different and stays separate.

Can I solve this problem by adding instead of subtracting?

+

No! You must follow the order of operations. The parentheses and subtraction are given in the problem, so you must distribute the negative sign first, then combine like terms.

What's the difference between 4x-4b and -4b+4x?

+

They're exactly the same! Addition and subtraction can be rearranged using the commutative property. Both expressions equal the same value.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Commutative, Distributive and Associative Properties questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations