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Writing Equivalent Equations

Writing Equivalent Equations

Author: Sophia Tutorial
Description:

Determine if equations are equivalent by solving each equation and comparing their solution.

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Tutorial
what's covered
  1. Equivalent Equations
  2. Determining if Two Equations are Equivalent

1. Equivalent Equations

In mathematics, we work with equivalent equations all the time. Think about the process for solving a multi-step equation. We might start with something such as 5x + 3 = 23 Using inverse operations, we create a series of equivalent equations in order to find a value for x.

5 x plus 3 equals 23

5 x equals 20
An equivalent equation
x equals 4
An equivalent equation

The equations above are all considered equivalent equations, because they have the same solution. In each equation, the solution is x = 4.


2. Determining if Two Equations are Equivalent

In order to determine if two equations are equivalent, we will solve each equation, and then compare their solutions. If their solutions are the same, we can say the equations are equivalent. If the solutions are not the same, we know that the equations are not equivalent.

Determine if the equations below are equivalent:

short dash 3 x plus 2 equals short dash 4

1 half x space plus 9 equals 8


Solve each equation separately:

short dash 3 x plus 2 equals short dash 4
1 half x space plus 9 equals 8
short dash 3 x equals short dash 6 Subtract 6 1 half x equals short dash 1 space space Subtract 9
x equals 2 Divide by short dash 3 x equals short dash 2 Multiply by 2

The solutions to our equations are x = 2 and x = –2. Since the solutions are not the same, the two equations are not equivalent.

summary
We can define equivalent equations as equations that have the same solution or solution set. To determine if two equations are equivalent to each other, you just need to solve each equation and then determine if their solutions are the same.