Question

how can you determine which property of equality is needed to isolate a variable and solve a given equation? explain.
a. use inverse relationships to \undo\ the operation.
b. use the same operation to \undo\ the operation.
c. use the distributive property to isolate the variable.
d. substitute the known values and simplify.

Explanation:

To isolate a variable in an equation, we use inverse operations (e.g., addition and subtraction are inverses, multiplication and division are inverses) to "undo" the operation acting on the variable. Option A says to use inverse relationships to undo the operation, which matches this concept. Option B is incorrect because using the same operation doesn't undo it (e.g., adding again doesn't undo an addition). Option C is incorrect as the Distributive Property is for expanding, not isolating variables. Option D is for checking solutions, not isolating variables.

Answer:

A. Use inverse relationships to "undo" the operation.