Equivalent Equations Worksheet
Grade 11 Algebra worksheet focusing on understanding and manipulating equivalent equations.
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Equivalent Equations Worksheet
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Read each question carefully and follow the instructions. Show all your work for full credit.
1. Which of the following equations is equivalent to 2x + 5 = 11?
2x = 6
x + 5 = 11
2x = 16
x = 6
2. Which operation applied to both sides of the equation 3x - 7 = 14 would result in an equivalent equation?
Multiplying by 3
Subtracting 7
Dividing by 3
Adding 7
3. Equations that have the same solution set are called equations.
4. To maintain an equivalent equation, any operation performed on one side of the equation must also be performed on the side.
5. Explain why adding the same number to both sides of an equation results in an equivalent equation.
6. For each equation, write two equivalent equations by applying a different operation each time.
a) 4x - 8 = 12
Equivalent Equation 1:
Equivalent Equation 2:
b) 7 + 2y = 15
Equivalent Equation 1:
Equivalent Equation 2:
Match each equation on the left with its equivalent equation on the right.
7. 5x + 3 = 18
a. x = 4
8. 2(x - 1) = 6
b. 5x = 15
9. x/3 + 2 = 5
c. x = 9
10. The equation 3x = 9 is equivalent to x = 3.
True
False
11. Multiplying both sides of an equation by zero always produces an equivalent equation.
True
False
12. The perimeter of a rectangle is 24 cm. If the length is 8 cm, write an equation to find the width (w) and then write an equivalent equation that solves for w.
Original Equation:
Equivalent Equation (solving for w):
13. Consider the equation 3x + 6 = 18.
a) What operation would you perform first to isolate the variable term?
b) Write the equivalent equation after performing that operation.