Question
Which of the following are equivalent expressions?
i) 3x + 9
ii) 3x
iii) 3(x + 3)
- i and iii
- i and iii
- ii and iv
- iv
Hint:
We are given three algebraic expressions. An algebraic expression can consist of a variable and a constant. We are asked to find which of them is an equivalent expression. For equivalent expressions, we have to rearrange the expression without changing the value of the expression.
The correct answer is: i and iii
The given expressions are
3x + 9
3x
3(x + 3)
For the first expression, as both are unlike terms, no further operation is possible. Unlike terms means terms having different variables or a variable and constant.
The variable of the first term is x, and it’s multiplied by 3. And 9 is added to the whole value. 9, cannot be added to the coefficient of x.
The second value is 3x. The term is same as the first term in first expression, but it doesn’t have a constant 9 added to it. So it changes the value of the expression. So the second expression is not equivalent to first expression. Same will happen if we compare second and third.
For the third expression, the terms in the bracket are like terms. But we can use distributive property to solve it further.
Distributive property: It says that the term outside the bracket, or in other words, in the multiplication of the bracket, gets distributed equally to the terms inside the bracket.
So we can write the third expression as
3(x + 3) = (3)x + (3)3
3(x + 3) = 3x + 9
If we see it’s the same as the first expression.
Therefore, the expressions “3x + 9” and “3(x + 3)” are equivalent expressions.
So option ‘i and iii’ is the right option.
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.
Related Questions to study
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