GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsEasy
A civil engineer is calculating the load on a bridge support. The load (L) in tons is given by the expression 5(x - 3) + 2x - 7, where 'x' is a variable representing traffic density. Simplify this expression.
- A7x + 8
- B7x - 22
- C3x - 10
- D7x - 10
Show answer & explanationAnswer & explanation
Correct answer: B. 7x - 22
First, distribute the 5: 5(x - 3) = 5x - 15. Then combine with the rest of the expression: 5x - 15 + 2x - 7. Combine like terms: (5x + 2x) + (-15 - 7) = 7x - 22.
Why the other options are wrong
- A. Incorrect constant term and sign mistake.
- C. Incorrectly combines the 'x' terms (5x - 2x).
- D. Incorrect constant term (-15 + 7 = -8, not -10).
Simplifying Algebraic Expressions
Rewriting an algebraic expression in a simpler, equivalent form by combining like terms and applying the distributive property.
- Use the distributive property to remove parentheses.
- Identify and combine like terms (terms with the same variable and exponent).
- Combine constant terms.
Memory trick: Distribute, then Combine, make it shine!