Question
What is the value of 10n + 6, 2(5n + 3), when the value of n = 1?
- 15
- 14
- 16
- 18
Hint:
We are given two algebraic expressions. An algebraic expression can consist of variables and constants. A variable doesn’t have a fixed value. A constant always has a fixed value. There is one variable ‘n’ in both the given expression. A value is assigned to the variable ‘n’. The value of n is 1. We have to substitute the value and find the final value of the given expressions.
The correct answer is: 16
The given expressions are 10n + 6 and 2(5n + 3)
The value of n = 1.
We have to substitute the value in both the expressions and find their respective values.
Let’s substitute the value in the first expression.
10n + 6 = 10(1) + 6
10n + 6 = 10 + 6
10n + 6 = 16
Now let’s substitute the value in the second expression.
2(5n + 3) = 2[5(1) + 3]
2(5n + 3) = 2(5 + 3)
2(5n + 3) = 2(8)
2(5n + 3) = 16
We can see that both have the same values.
Now let’s expand the second expression using the distributive property. Distributive property means the quantity outside the bracket is distributed equally to the terms inside the bracket.
2(5n + 3) = 10n + 6
So we can see that the value is the same as the first expression.
So both the expressions are equivalent. Equivalent expressions have the same variable and, on rearranging the expression, give the same terms and same operation.
Therefore, the value of given expressions is 16.
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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