Solving Proportions and Equations

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal. For example, if a/b = c/d, then a, b, c, and d are in proportion.

Front

How do you solve a proportion?

Back

To solve a proportion, cross-multiply the terms. For example, if a/b = c/d, then ad = bc.

Front

What does it mean to isolate a variable in an equation?

Back

Isolating a variable means rearranging the equation so that the variable is on one side and all other terms are on the other side.

Front

What is the first step in solving the equation 10x + 9 = 4x - 9?

Back

The first step is to get all terms involving x on one side and constant terms on the other side.

Front

What is the solution to the equation 10x + 9 = 4x - 9?

Back

x = -3.

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What is the solution to the equation 4(3r + 4) = -8(2r + 5)?

Back

r = -2.

Front

What is the definition of a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one and can be written in the form ax + b = 0.

Front

What does it mean if an equation has infinitely many solutions?

Back

It means that there are an infinite number of values for the variable that satisfy the equation, often occurring when both sides of the equation are identical.

Front

What is the solution to the proportion 3/4 = x/16?

Back

x = 12.

Front

What is the definition of a variable in mathematics?

Back

A variable is a symbol used to represent an unknown value in mathematical expressions and equations.