Check All Equations That Are Equivalent

Checking Equivalent Equations

In mathematics, two equations are said to be equivalent if they have the same solution set. This means that any value that satisfies one equation also satisfies the other equation.

There are a few different ways to check whether two equations are equivalent. One way is to solve both equations for the same variable. If the solutions are the same, then the equations are equivalent.

For example, consider the following two equations:

x + 2 = 7 x = 5 

Solving the first equation for x, we get x = 7 - 2. Substituting this into the second equation, we get (7 - 2) = 5. This is true, so the two equations are equivalent.

Another way to check whether two equations are equivalent is to use the following steps:

1. Perform the same operations on both sides of both equations. This can include adding, subtracting, multiplying, dividing, or combining like terms.
2. Simplify both sides of both equations.
3. Compare the simplified versions of the two equations. If they are the same, then the equations are equivalent.

For example, consider the following two equations:

x^2 + 2x - 3 = 0 (x + 3)(x - 1) = 0 

Multiplying both sides of the first equation by (x + 3)(x - 1), we get

(x + 3)(x - 1)(x^2 + 2x - 3) = 0 

Expanding the left side, we get

x^3 + x^2 - 3x - 3x^2 - 6x + 3 = 0 

Combining like terms, we get

-4x^2 - 9x + 3 = 0 

This is the same as the second equation, so the two equations are equivalent.

Related Questions

Here are some related questions that you may be asked about checking equivalent equations:

• What are the different ways to check whether two equations are equivalent?
• How do you use the steps to check whether two equations are equivalent?
• What are some examples of equivalent equations?

Answers

• There are two main ways to check whether two equations are equivalent: solving both equations for the same variable, and using the steps to check whether two equations are equivalent.
• The steps to check whether two equations are equivalent are as follows:
  1. Perform the same operations on both sides of both equations.
  2. Simplify both sides of both equations.
  3. Compare the simplified versions of the two equations.
• Some examples of equivalent equations include:
  • x + 2 = 7 and x = 5
  • x^2 + 2x - 3 = 0 and (x + 3)(x - 1) = 0
  • 2x + 3 = 5 and x + 1.5 = 2.5

I hope this helps!