Math Problem Statement
Solution
Let me analyze and solve each question in detail:
Question 1:
Subtract:
Solution:
- Distribute the negative sign to the second parenthesis:
- Combine like terms:
- For :
- For constants:
Final Answer:
Question 2:
Rewrite the expression without parentheses.
Solution:
- Distribute the negative sign to :
- Combine like terms:
- For :
- The constant remains .
Final Answer:
Question 3:
A student received a coupon for 14% off the total purchase price at a clothing store. Let be the original price of the purchase. The expression represents the new price. Write an equivalent expression to show another way to represent the new price.
Solution:
Factor out from :
Simplify:
Final Answer:
Question 4:
Simplify the expression:
Solution:
- Distribute the negative sign to the second parenthesis:
- Combine like terms:
- For :
- For constants:
Final Answer:
Question 5:
Each month, a shopkeeper spends dollars on rent and electricity. If he spends dollars on rent, how much does he spend on electricity?
Solution:
- Total expense = Rent + Electricity:
Rent =
Electricity = Total expense - Rent:
- Simplify:
Distribute the negative sign:
Combine like terms:- For :
- For constants:
Final Answer:
Summary of Answers:
Would you like detailed explanations for any specific question?
Here are 5 related questions to practice:
- Simplify .
- Rewrite without parentheses.
- Write an equivalent expression for .
- Simplify .
- A shopkeeper spends dollars, with on rent. How much does he spend on electricity?
Tip: Always distribute negative signs carefully when simplifying expressions!
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Math Problem Analysis
Mathematical Concepts
Algebra
Simplification
Factoring
Combining Like Terms
Formulas
Distributive Property: a(b + c) = ab + ac
Factoring: ab - ac = a(b - c)
Theorems
Basic Properties of Arithmetic and Algebra
Suitable Grade Level
Grades 6-8
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