Solving & Graphing Inequalities A-REI 1, 3, 10 A-CED 1, 2 N-Q 1 A-SSE 1 F-IF 2, 6

Objective - To write, solve, graph and interpret simple, compound, and absolute value inequalities.

The ≠ (not equal to) sign is also an inequality symbol. INEQUALITIES The four basic inequality symbols are: The ≠ (not equal to) sign is also an inequality symbol.

VARIABLE SYMBOL NUMBER Writing an inequality FORM is important! You should ALWAYS write your inequality in the form: VARIABLE SYMBOL NUMBER i.e. 5 < x should be written x > 5

Graphing an inequality The inequality symbols tell us the type of “dot” to use: Use an open dot Use a closed dot

Graphing an inequality Using the correct form tells us the direction of the arrow!

Graphing an inequality Equations Inequalities Solve and graph. Solve and graph. -3 -2 -1 0 1 2 3 4 -3 -2 -1 0 1 2 3 4 One Solution Infinite Solutions

Graph the following inequalities. 1) 3) -3 -2 -1 0 1 2 3 4 -3 -2 -1 0 1 2 3 4 2) 4) -3 -2 -1 0 1 2 3 4 -3 -2 -1 0 1 2 3 4

Solve and graph the inequalities. 1) 2) -10 0 10 -1 0 1 2 3

Solve and graph the inequalities. 3) 4) -13 0 0 12

Solve and graph the inequalities. 1) 2) 0 5 -6 0 6

For what values of x is the statement true? x = 3 x = 2 x = 1 x = 0 Inequalities transform like equations except... For what values of x is the statement true? x = 3 x = 2 x = 1 x = 0 reverse x = -1 x = -2 we know ...

Inequalities transform like equations except... When multiplying or dividing by a negative number you must reverse (flip) the inequality. -4 -3 -2 -1 0 1 2 3 4 Negative side Positive side Large is small Large is large reverse

Solve and graph the inequalities. 1) 2) -6 0 -21 0

Solve and graph the inequalities. 3) 4) -6 0 -12 0