Question
Are 6(n + 3) – 4 and 6n + 14 equivalent expressions?
- Yes
- No
- Either yes or no
- None of the above
Hint:
We are given two algebraic expressions. An algebraic expression can consist of a variable and a constant. We are asked to find if the equivalent expressions. For equivalent expressions, we have to rearrange the expression without changing the value of the expression
The correct answer is: Yes
The given expressions are 6(n + 3) – 4 and 6n + 14.
Let’s see the first expression.
The terms inside the bracket are unlike terms. Unlike terms do not have same variable. So, no further operation is possible for the terms inside the bracket.
For the second expression, both are unlike terms. So, no further operation is possible.
We can solve the first expression further if we use the distributive property.
Distributive property says that, the term outside the bracket or in other words, in multiplication with bracket, can be disturbed equally inside the bracket.
So the expression becomes
6(n + 3) – 4 = [(6)n + (6)3] – 4
6(n + 3) – 4 = 6n + 18 – 4
6(n + 3) – 4 = 6n + 14
If we see it’s the same as the second expression. So we can say that both the expressions '6(n + 3) – 4’ and '6n + 14’ are equivalent expressions.
So the right option is the option that says ‘yes’.
For such questions, we should be familiar with the different properties required to perform algebraic expression. At the same time we should know the basic rules of operations of algebraic expression.
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