Equivalent linear algebraic expressions

More about equivalent linear algebraic expressions

With examples like Question 1 (multiple choice) we can use trial and error to make a correct choice.

Which one of the four expressions will lead to the same result as 2 − 3t when the same number is substituted into both expressions?

For example when t = 0, 2 − 3t = 2 − 3 × 0 = 2 − 0 = 2.

3 − 2t = 3 − 2 × 0 = 3 − 0 = 3 ≠ 2

3t − 2 = 3 x 0 − 2 = 0 − 2 = −2 ≠ 2

−2 + 3t = −2 + 3 x 0 = −2 + 0 = −2 ≠ 2

−3t + 2 = −3 x 0 + 2 = 0 + 2 = 2

So 2 − 3t is equivalent to −3t + 2.

This method might be time consuming if you get more than one correct answer. You will need to try another number.

For example, if t = −1 then 2 − 3t = 5.

Also, 3 − 2t = 5 and −3t + 2 = 5.

But, 2 − 3t is not equivalent to 3 − 2t.

You will only ever need to try up to two numbers if the expressions are linear. Why?

Not equivalent expressions

Graphical explanation