INEQUALITIES Solving Inequalities Graphing Solution Sets INEQUALITY SYMBOLS

INEQUALITIES Solving Inequalities & Graphing Solution Sets

INEQUALITY SYMBOLS < - less than > - greater than < - less than but equal to > - greater than but equal to

EQUATIONS VS. INEQUALITIES • Equations only have one solution. 3 x – 6 = -18 +6 = + 6 3 x = -12 3 3 x = -4 The solution to the equation is -4. • Inequalities have an infinite number of solutions which is called the solution set of the inequality. An inequality sign is used instead of an equal sign. 3 x – 6 > -18 + 6 > +6 3 x > -12 3 3 x > -4 Every number greater than -4 is a solution to this inequality. Solution set ( -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7……. )

Graphing the Solution Set of an Inequality The solution set of an inequality is graphed on a number line. The inequality symbols < or > are denoted by an open circle on the number line. The inequality symbols < or > are denoted by a closed circle on the number line. Examples X > -2 _________________ -2 X < 10 0 _________________ -10 X< 5 0 10 _________________ -5 X > -1 2 0 5 _________________ -1 0 1

SOLVING ONE-STEP INEQUALITIES & GRAPHING THE SOLUTION SET • Example 1 • Example 2 a+7< 4 12 m > -60 12 - 7 < -7 12 m > -5 a < -3 Graphing the solution set __________________________________ -3 0 3 -5 0 5 What numbers are part of this solution set? What numbers are not part of the solution set?