4.1.1 – Solving Inequalities

• All equations we have solved are considered problems of equality– Involves some kind of equal sign

• On the other hand, we could have inequalities which are problems not involving the use of equal signs

Types of Inequalities

• < = Less than• ≤ = Less than or equal to• > = Greater than• ≥ = Greater than or equal to

Linear Inequalities

• A linear inequality is an inequality with a linear component (IE, think y = mx + b for linear)

• Solutions of the inequality are values that make the inequality true for the given variable

Solving Linear Inequalities

• Similarities to equations:– Will still use inverse operations– Isolate the variable of interest– Treat other letters or numbers as constants

• Differences:– Solutions will likely be many numbers– If multiply or divide by a negative number, must

flip the sign

• Example. Solve the inequality 2p > 12.

• Example. Solve the inequality 4x + 5 ≤ 17

Flipping the Sign

• Example. Solve the inequality -5y + 2 > -13

• Example. Solve the inequality 7 – 4x < 1 – 2x– Get variables to same side, first

Graphing Solutions on Number Line

• Once we solve the inequality, we may plot the solutions on a number line

• If x > a (or, whatever variable), open dot, then point arrow to the right

• If x < a (or, whatever variable), open dot, then point arrow to the left

• If x ≥ a (or, whatever variable), closed dot, then point arrow to the right

• If x ≤ a (or, whatever variable), closed dot, then point arrow to the left

• Example. Solve the inequality 4 – x < 5. Then plot your solution.

• Example. Solve the inequality 2x – 3 ≥ x. Then plot your solution.

• Assignment• Pg. 175• 4-9, 23-28, 29-32