Grade 12 Math: Equivalent Equations
This worksheet focuses on understanding and manipulating equivalent equations, a fundamental concept in advanced algebra.
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Equivalent Equations Worksheet
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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?
3x = 5
3x = 15
x - 5 = 10/3
x = 10
2. The equation 2(x + 4) = 14 is equivalent to:
2x + 4 = 14
x + 4 = 7
2x = 10
All of the above
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.
True
False
9. Adding a constant to both sides of an equation always produces an equivalent equation.
True
False
Match the original equation with its equivalent equation.
10. 5x - 2 = 13
a. x = 3
11. (x + 1)/2 = 4
b. 5x = 15
12. 3x + 6 = 18
c. x + 1 = 8
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