Practice Equivalence Transformation in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Operations applied to both sides of an equation that transform its form while leaving its solution set completely unchanged.
Whatever you do to one side, do to the other — the balance stays true.
Showing a random 20 of 59 problems.
Example 1
easySolve using an equivalence transformation.
Example 2
easySolve .
Example 3
hardSolve the system using equivalence transformations.
Example 4
easyTrue or false: subtracting the same expression from both sides of an equation always yields an equivalent equation.
Example 5
mediumPriya and Sam have exactly the same amount of money. Each of them spends dollars on lunch. Priya now has dollars. How many dollars does Sam have now?
Example 6
mediumWhy is squaring both sides of an equation NOT always an equivalence transformation?
Example 7
challengeFind all satisfying and state any restrictions.
Example 8
mediumSolve .
Example 9
mediumFill the blank so the solution is :
Example 10
mediumSolve .
Example 11
mediumBen solves like this: he divides the left side by but subtracts on the right, writing . Find his mistake and enter the correct value of .
Example 12
mediumWhy is multiplying both sides of by usually safe here?
Example 13
mediumSolve .
Example 14
hardSolve and identify any extraneous solutions.
Example 15
mediumTrue or false: multiplying both sides of by yields an equivalent equation.
Example 16
mediumFill in: To remove the fraction in , you can ___ both sides by 3 first or after adding 1.
Example 17
mediumShow that and are equivalent equations.
Example 18
easySolve .
Example 19
hardSolve the inequality .
Example 20
mediumSolve .