Topic 8: Proportions and Literal Equations

Front

What is a proportion?

Back

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

Front

How do you solve for a variable in a literal equation?

Back

To solve for a variable in a literal equation, isolate the variable on one side of the equation using algebraic operations.

Front

What does it mean if an equation has infinite solutions?

Back

An equation has infinite solutions if any value of the variable satisfies the equation, often occurring when the equation simplifies to a true statement.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution if there is no value of the variable that can satisfy the equation, often occurring when the equation simplifies to a false statement.

Front

What is the first step in solving the equation 3x + 15 = 3(x + 5)?

Back

The first step is to distribute the 3 on the right side of the equation.

Front

What is the solution to the equation xy + w = 9 for y?

Back

The solution for y is y = (9 - w) / x.

Front

What is the definition of a literal equation?

Back

A literal equation is an equation that involves two or more variables.

Front

How can you check if two ratios form a proportion?

Back

You can check if two ratios form a proportion by cross-multiplying and seeing if the products are equal.

Front

What is the significance of the term 'literal' in literal equations?

Back

The term 'literal' refers to the use of letters to represent variables or constants in the equation.

Front

What is the process of isolating a variable?

Back

Isolating a variable involves rearranging the equation to get the variable alone on one side.