"Expressions" that represent the same value may appear in several different forms,
referred to as equivalent expressions.

When determining equivalent expressions:
take your time and LOOK CAREFULLY!
Some expressions may not LOOK equivalent at first glance,
but upon further examination they will be equivalent.

 If you are having trouble determining if expressions are equivalent, plug the same number into each expression to see if each expression gives the same result. NOTE: Avoid choosing the numbers 0 and 1 for substituting.

The number 3 will be used for the numerical checks in the following examples.

 Are these expressions equivalent?     7x + 2x and 14x Numerical check 7(3) + 2(3) = 27 14(3) = 42 27 ≠ 42 Algebraic check: 7x + 2x = 9x 9x ≠ 14x Not Equivalent!

 Are these expressions equivalent?     5(x - 2) and 5x - 10 Numerical check 5(3 - 2) = 5 5(3) - 10 = 5 CHECK Algebraic check: 5(x - 2) = 5x - 10 Distributive Property CHECK Equivalent!

 Are these expressions equivalent?     6(3x) and 9x Numerical check 6(3(3)) = 54 9(3) = 27 54 ≠ 27 Algebraic check: 6(3x) = 18x 9x ≠ 18x Not Equivalent!

 Which of the following expressions are equivalent to 6(x + 2)?
The distributive property shows that 6(x + 2) equals 6x + 12. Also, 6(3 + 2) = 6(5) = 30
 Expression Y/N Numerical Check Algebraic Check a) 6x + 2 NO 6(3) + 2 = 20 ≠ 30 6x + 2 ≠ 6(x + 2) = 6x + 12 b) 3x + 6 + 3x + 6 YES 3(3) + 6 + 3(3) + 6 = 30 3x + 6 + 3x + 6 = 6x + 12 c) 6x + 12 YES 6(3) + 12 = 30 6x + 12 = 6(x + 2) = 6x + 12 d) 3(x + 2) + 3(x + 2) YES 3(3 + 2) + 3(3 + 2) = 30 3(x + 2) + 3(x + 2) = 3x + 6 + 3x + 6 = 6x + 12 e) 3(x + 2) + 3x NO 3(3 + 2) + 3(3) = 24 ≠ 30 3(x + 2) + 3x = 3x + 6 + 3x = 6x + 6 ≠ 6x + 12

The graphing calculator can also be used to evaluate expressions.
Click on the link at the right to see the possibilities.