Question
Which of the following expressions are equivalent?
i) 8x – 4
ii) 4(2x – 1)
iii) 4x
- i and ii
- ii and iii
- iii and i
- i
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 ii
The given expressions are
8x – 4
4(2x – 1)
4x
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 8. And 4 is subtracted from the whole value. 4, cannot be subtracted the coefficient of x.
For the second expression, the terms in the bracket are unlike 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
4(2x – 1) = (4)2x – (4)1
4(2x – 1) = 8x – 4
If we see it’s the same as the first expression.
Now, let’s see the third expression. It cannot be equal to the first expression, as the first expression has a coefficient 8 for the variable. And 4 is subtracted from the whole quantity ‘8x’. It cannot be subtracted just from the coefficient as both are unlike terms.
Therefore, the expressions “8x - 4” and “4(2x – 1)” are equivalent expressions.
So option ‘i and ii’ 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.
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