GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsEasy
A technician is installing a new network. The total length of cable, L, in meters, required for the installation is given by the expression 3(x + 5) - 2x, where x represents the number of workstations. Which of the following expressions is equivalent to L?
- A5x + 5
- B5x + 15
- Cx + 5
- Dx + 15
Show answer & explanationAnswer & explanation
Correct answer: D. x + 15
To find the equivalent expression, distribute the 3 into the parenthesis and then combine like terms. 3(x + 5) - 2x becomes 3x + 15 - 2x, which simplifies to x + 15.
Why the other options are wrong
- A. This option incorrectly adds 3x and 2x instead of subtracting them.
- B. This option incorrectly adds 3x and 2x and correctly keeps the constant term 15.
- C. This option incorrectly combines 3x - 2x to x but drops the constant term 15.
Simplifying Algebraic Expressions
The process of rewriting an algebraic expression in a simpler, equivalent form by combining like terms and applying the order of operations.
- Involves distribution, combining like terms.
- Resulting expression has fewer terms or is easier to read.
- Does not change the value of the expression.
Memory trick: Distribute, then Combine - Don't Forget the Signs!