Identify Equivalent Equations

Front

What is an equivalent equation?

Back

An equivalent equation is an equation that has the same solution as another equation. For example, if you have the equation 2x + 3 = 7, an equivalent equation would be 2x = 4.

Front

How can you create an equivalent equation?

Back

You can create an equivalent equation by performing the same operation on both sides of the equation, such as adding, subtracting, multiplying, or dividing.

Front

What does it mean to isolate a variable?

Back

Isolating a variable means to manipulate an equation so that the variable is on one side of the equation by itself.

Front

If 5 + n = 10, what is the value of n?

Back

n = 5, because if you subtract 5 from both sides, you get n = 10 - 5.

Front

Which of the following is NOT equivalent to 5 + n = 10? 5 + n - n = 10 - n, 5 + n - 5 = 10 - 10, 5 + n - 5 = 10 - 5, 5 + n + 3 = 10 + 3.

Back

5 + n - 5 = 10 - 10 is NOT equivalent.

Front

What is the first step to solve the equation 3x + 4 = 10?

Back

Subtract 4 from both sides to isolate the term with the variable: 3x = 6.

Front

What is the solution to the equation 4x = 20?

Back

x = 5, because you divide both sides by 4.

Front

What does it mean for two equations to be equivalent?

Back

Two equations are equivalent if they have the same solution set.

Front

If you have the equation x - 2 = 3, what is an equivalent equation?

Back

An equivalent equation is x = 5, obtained by adding 2 to both sides.

Front

What operation can you perform to both sides of an equation without changing its equality?

Back

You can add, subtract, multiply, or divide both sides by the same non-zero number.