Solving Proportions

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal.

Front

How do you solve a proportion?

Back

To solve a proportion, you can cross-multiply the two ratios and then solve for the variable.

Front

What does cross-multiplication involve?

Back

Cross-multiplication involves multiplying the numerator of one ratio by the denominator of the other ratio.

Front

What is the first step in solving the equation -6/3 = (2x + 6)/7?

Back

The first step is to cross-multiply: -6 * 7 = 3 * (2x + 6).

Front

What is the solution to the equation -6/3 = (2x + 6)/7?

Back

The solution is x = -10.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to get the variable by itself on one side of the equation.

Front

What is the solution to the proportion 3/5 = (x - 4)/5?

Back

The solution is x = 7.

Front

What does it mean to simplify an answer?

Back

To simplify an answer means to express it in its simplest form, reducing any fractions or combining like terms.

Front

How do you solve the equation 7/(x - 7) = 5/(x - 9)?

Back

Cross-multiply to get 7(x - 9) = 5(x - 7) and then solve for x.

Front

What is the solution to the equation 7/(x - 7) = 5/(x - 9)?

Back

The solution is x = 14.