Types of solutions equations and inequalities

Front

What is a solution to an equation?

Back

A solution to an equation is a value that makes the equation true when substituted for the variable.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution if there are no values that can be substituted for the variable to make the equation true.

Front

What does it mean if an equation has one solution?

Back

An equation has one solution if there is exactly one value that can be substituted for the variable to make the equation true.

Front

What does it mean if an equation has infinite solutions?

Back

An equation has infinite solutions if any value substituted for the variable makes the equation true.

Front

What is the first step in solving a linear equation?

Back

The first step is to simplify both sides of the equation, if necessary, by distributing and combining like terms.

Front

How do you determine if two expressions are equivalent?

Back

Two expressions are equivalent if they yield the same value for all values of the variable.

Front

What is the significance of the coefficients in an equation?

Back

Coefficients determine the weight of the variable in the equation and affect the slope of the line when graphed.

Front

What is the role of constants in equations?

Back

Constants are fixed values that do not change and can shift the graph of the equation up or down.

Front

How can you tell if an equation is linear?

Back

An equation is linear if it can be written in the form y = mx + b, where m and b are constants.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by a sum.