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# Equations and Inequalities

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# Equivalent Equations

Two equations are said to be equivalent if they have exactly the same solutions.

### Sample Problems

- The equations
*x*= 1 and 2*x*= 2 are equivalent, since the only solution to either equation is 1. - The equations 2
*x*= 0 and 3*x*= 0 are equivalent, since the only solution to either equation is 0. - The equations
*x*= 1 and*x*= 2 are not equivalent, since their solutions, 1 and 2, respectively, differ.