GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsEasy
A civil engineer is designing a ventilation system for a building. The airflow rate (R) in cubic feet per minute (cfm) through a duct is given by the expression 5(3x - 2) + 2(x + 7), where 'x' is a design parameter. Which of the following expressions is equivalent to the airflow rate R?
- A13x + 24
- B17x + 24
- C13x + 4
- D17x - 4
Show answer & explanationAnswer & explanation
Correct answer: C. 13x + 4
To simplify the expression, first distribute the constants into the parentheses: 5(3x - 2) = 15x - 10 and 2(x + 7) = 2x + 14. Then combine like terms: (15x + 2x) + (-10 + 14) = 17x + 4.
Why the other options are wrong
- A. This results from a calculation error in the coefficient of x (15x + 2x = 17x, not 13x).
- B. This results from a sign error in the constant terms (-10 + 14 = 4, not 24) or distribution error (5*2=10, 2*7=14, 10+14=24).
- D. This results from a sign error in the constant terms (-10 - 14).
Simplifying Algebraic Expressions
The process of rewriting an algebraic expression in a simpler, more compact form by combining like terms and applying the order of operations.
- Use the distributive property to remove parentheses.
- Combine like terms (terms with the same variable and exponent).
- Follow the order of operations (PEMDAS/BODMAS).
Memory trick: Simplify: Distribute, then Collect!