Equivalent Equations

Two equations are equivalent if they have the same solution.

2x − 3 = 3x + 2    x = −5

x + 3 = −2   x = −5

Criteria for Equivalence of Equations

1. If two members of an equation are added or subtracted by the same amount, the equation is equivalent to that given.

x + 3 = −2

x + 3 − 3 = −2 − 3    

  x = −5

2. If two members of an equation are multiplied or divided by the same number (nonzero), the equation is equivalent to that given.

5x + 10 = 15

(5x + 10) : 5 = 15 : 5    

 x + 2 = 3    ;

 x + 2 − 2 = 3 − 2

x = 1