Graphing and Solving Inequalities Notes

Algebra I 6.1 ? 6.3 Graphing & Solving Inequalities

Name ______________________ Date _______________ Block __

GRAPHING INEQUALITIES

The graph of an inequality with one variable is the set of points that represent all solutions of the inequality.

To graph the solution to an inequality with one variable: Use an open circle for < or > Use a closed circle for or Remember to label your number line (label UNDER the number line)

Examples Graph of x < 3

Graph of x -1

Your Turn Graph the following inequalities.

1. x > 4

2. y -2

3. p < 5

4. m -3

SOLVING INEQUALITIES WITH ONE VARIABLE

Solving inequalities is much like solving equations. The goals are still the same:

Get the variable on one side. Get the constants on the other side.

There is ONE BIG DIFFERENCE ...

When you multiply or divide by a negative, MUST FLIP the inequality symbol!

To check solutions: If your inequality symbol is < or >, use the solution o if your answer is x > -3, use -3 since -3 is in the set of answers If your inequality symbol is < or >, use a number that makes the statement true o if your answer is x > 3, pick a number greater than 3 (like 4) o if your answer is x < 3, pick a number smaller than 3 (like 2) If your answer is a fraction, use the next integer to check

Examples: Solve each inequality. Check your answer. Then, graph your solution.

1. x ? 3 < 2

2. -3x > 12

3.

x - -30

5

Multi-Step Inequalities

We use the same steps to solve multi-step inequalities as we did to solve multi-step equations (just remember: with inequalities, when you multiply or divide by a negative, flip the inequality symbol).

Steps to solving inequalities: ? Isolate the variable on the LEFT side of the inequality. ? Add or subtract to isolate the variable term. ? Multiply or divide to isolate the variable. ? Remember to FLIP the symbol when you multiply or divide by a negative!

Try These: 1. 3x ? 7 < 8

2. -3(w + 12) < 0

3. 4 ? 2m > 7 ? 3m

4. 6x + 3 3(x + 2)

5. 2x -14 > 4x + 4

6. 8 - 2(3x - 4) > 10x - 20

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