Equivalent linear algebraic expressions
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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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