Solving Inequalities and their Solving Inequalities and their GraphsGraphs

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Inequalities and their GraphsInequalities and their Graphs

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What is a good definition for Inequality?

An inequality is a statement that two expressions are not equal

SymbolsSymbols

Less than

Greater than

Less than OR EQUAL TO

Greater than OR EQUAL TO

Solving Inequalities Solving Inequalities

• When you are solving inequalities using addition and subtraction, you use the same steps you would use to solve equations.

• Once you find a solution of an inequality, you graph the solution using a number line.

Terms you see and need to know to graph inequalities correctly

Notice open circles– only if it’s greater or less than.

< less than

> greater than

Terms you see and need to know to graph inequalities correctly

Notice colored in circles– only if its equal to or less than/greater than

≤ less than or equal to

≥ greater than or equal to

Your solutions can have a range of answers……

-5 -4 -3 -2 -1 0 1 2 3 4 5

All real numbers less than 2

x< 2

Inequalities and their GraphsInequalities and their Graphs

Let’s work a few together

3

Notice: when variable is on left side, sign shows direction of solution

Inequalities and their GraphsInequalities and their Graphs

Let’s work a few together

-2

Notice: when variable is on left side, sign shows direction of solution

Color in circle

Solving an InequalitySolving an Inequality

Solving a linear inequality in one variable is much like solving a linear equation in one variable. Isolate the variable on one side using inverse operations.

x – 3 < 5Solve using addition:

+3 +3

x < 8

Solving Using SubtractionSolving Using Subtraction

Subtract the same number from EACH side.

4x-6 -6

-5 -4 -3 -2 -1 0 1 2 3 4 5

Solve then graph the solution.