Solving Inequalities in One Variable

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What does it mean to solve an inequality?

Back

To solve an inequality means to find all values of the variable that make the inequality true.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that satisfy the inequality.

Front

How do you graph an inequality on a number line?

Back

To graph an inequality, use an open circle for < or > and a closed circle for ≤ or ≥, then shade the appropriate side of the circle.

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows that one expression is greater than or less than another.

Front

What does it mean to isolate a variable?

Back

To isolate a variable means to manipulate an equation or inequality so that the variable is on one side by itself.

Front

How do you solve the inequality 12 ≥ 15 - 6y?

Back

Rearrange to get 6y ≤ 3, then divide by 6 to find y ≥ ½.

Front

What is the first step in solving the inequality 4x + 3 ≤ -6?

Back

Subtract 3 from both sides to get 4x ≤ -9.

Front

What does the term 'at least' indicate in an inequality?

Back

'At least' indicates that the value can be equal to or greater than a certain number.

Front

What does the term 'more than' indicate in an inequality?

Back

'More than' indicates that the value must be greater than a certain number, not equal to it.