Equivalent linear algebraic expressions

Equivalent linear algebraic expressions

Question 1

Which expression is equivalent to 2 − 3t ?

a

3 − 2t

b

3t − 2

c

−2 + 3t

d

−3t + 2

Solution

The linear expression 2 − 3t can be thought of as the sum of two terms: 2 and − 3t.

That is, 2 − 3t = 2 + (−3t ).

The order of addition does not matter.

2 + (−3t ) = (−3t ) + 2 for all values of t.

You do not need the brackets in this second expression.

2 + (−3t ) = −3t + 2 for all values of t.

So we can say 2 + (−3t ) is equivalent to −3t + 2.

So the answer is d.

You can do a check of your answer by substituting in a value for t. No matter what value you choose, equivalent expressions will always give the same answer. It must be true for every number you substitute.

For example, let t = 1.

Then 2 − 3t = 2 − 3 = −1

and −3t + 2 = −3 + 2 = −1.

Consider one more.

Let t = 2.

Then, 2 − 3t = 2 − 6 = −4

and −3t + 2 = −6 + 2 = −4.

  

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Not equivalent expressions