Grade 12 Math: Equivalent Equations

Equivalent Equations Worksheet

Carefully read each question and follow the instructions. Show all your work for full credit. Remember that equivalent equations have the same solution set.

1. Which of the following equations is equivalent to 3x - 5 = 10?

2. The equation 2(x + 4) = 14 is equivalent to:

3. Equations that have the same solution set are called   equations.

4. To maintain equivalence, any operation performed on one side of an equation must also be performed on the   side.

5. The operation of adding the same number to both sides of an equation is an example of a(n)   property of equality.

6. Explain why multiplying both sides of an equation by zero does NOT result in an equivalent equation.

7. Consider the equation 2x + 1 = 5. Draw a simple diagram, like a balance scale, to represent this equation. Then, draw a diagram for an equivalent equation formed by subtracting 1 from both sides.

8. The equation x^2 = 9 is equivalent to x = 3.

9. Adding a constant to both sides of an equation always produces an equivalent equation.

Match the original equation with its equivalent equation.