Which expression is equivalent to a + 9a + 5a? -13a 15a Submit Answer 1 + 14a a + 14
The Correct Answer and Explanation is:
Correct Answer: 15a
Explanation:
The given expression is a + 9a + 5a. To find an equivalent expression, one must simplify it by combining like terms.
In algebra, like terms are terms that contain the same variable raised to the same power. In this expression, all three terms—a, 9a, and 5a—are like terms because they all contain the variable ‘a’ raised to the first power (even though the exponent ‘1’ is not explicitly written).
The number in front of a variable is called the coefficient. To combine like terms, one simply adds or subtracts their coefficients.
- The term a has an implied coefficient of 1. So, a is the same as 1a.
- The term 9a has a coefficient of 9.
- The term 5a has a coefficient of 5.
The process of simplification involves adding these coefficients together while keeping the variable part the same.
- Identify the coefficients: 1, 9, and 5.
- Add the coefficients: 1 + 9 + 5.
- Perform the addition: 1 + 9 = 10, and 10 + 5 = 15.
The sum of the coefficients is 15. This number becomes the new coefficient for the common variable ‘a’.
Therefore, the simplified expression is 15a.
This concept is similar to combining physical objects. If you have one apple (a), then receive nine more apples (9a), and then another five apples (5a), you would have a total of fifteen apples (15a). The identity of the object (the apple, or ‘a’) does not change, only its quantity. The other options are incorrect because they either misinterpret the initial term a as the number 1 (as in 1 + 14a) or fail to combine all like terms correctly.
