1-5 Solving Inequalities Solve and graph inequalities by using properties of inequalities.

Graphing Inequalities Open dot for < or > Closed dot for ≥ or ≤ If the inequality symbol is open toward the variable, shade to the right. If the inequality symbol is pointed toward the variable, shade to the left.

Properties of Inequalities If you multiply or divide both sides of an inequality by a negative number, the symbol flips.

Solving Use inverse operations −3 2𝑥−5 +1≥4 −6𝑥+15+1≥4 −6𝑥+16≥4 −6𝑥≥−12 𝑥≤2 Graph the solution

No Solution or All Real Numbers There is no solution if all variables cancel and the statement is false. Ex: -2 > 7 (no variables and we know that -2 is not greater than 7) All real numbers are solutions if all variables cancel and the statement is true. Ex: -15 ≤ 8 (no variables and it is true that -15 is less than 8) Same as infinitely many solutions

Compound Inequality Consists of two distinct inequalities joined by the word and or the word or

Using the word “And” Contains the overlap of the graphs of two inequalities that form a compound inequality. EX: x ≥ 3 and x ≤ 7 Can also be written 3 ≤ x ≤ 7 This is only for a compound inequality using the word “and”

Using the word “Or” Contains each graph of the two inequalities that form the compound inequality. Used when there is no overlap. EX: x < -2 or x ≥ 1

Solving A solution to a compound inequality involving and is any number that makes both inequalities true. EX: -3 ≤ m – 4 < -1 Isolate the variable by adding 4 to each piece -3 + 4 ≤ m – 4 + 4 < -1 + 4 1 ≤ m < 3

Solving A solution to a compound inequality involving or is any number that makes either inequality true. You must solve each inequality separately. EX: 3t + 2 < -7 or -4t + 5 < 1 3t < -9 or -4t < -4 t < -3 or t > 1

Assignment Odds p.38 #27-31, 39-43