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Write an expression having only two terms that is equivalent to 2x – 3. Explain how you wrote the expression and how you can check that it is equivalent.

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Answer:

The expression has a variable with a coefficient (constant) and a constant. Therefore, to create a new expression with 2 terms, take out a constant and use parentheses:

The most obvious number to take out is either 2 or 3 since those are the constants in the expression:

Taking out the constant 3:

[tex]2x-3= 3\left(\dfrac23x-1\right)[/tex]

or taking out the constant 2:

[tex]2x-3= 2\left(x-\dfrac32\right)[/tex]

However, you can choose to take out any value, as long as it's a number and not a variable:

[tex]2x-3= \dfrac12\left(4x-6\right)[/tex]

[tex]2x-3= \dfrac14\left(8x-12\right)[/tex]

To check that it is equivalent, expand the brackets.
An equivalent expression would be for example:
3 ((2/3) x - 1).
In order to write it, what is done is that the common factor is taken out three of the expression.
To check which is the same expression, you can multiply three to both terms of the equation:
3 ((2/3) x - 1) = (3 * (2/3) x - 3 * 1) = ((6/3) x - 3) = (2x - 3).
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