1 st Quarter Review, Day 3 Test is Friday!!!

Graphing Inequalities Use an open circle for > and < Use a closed circle for =, ≤, and ≥ “shade in” the direction of the inequality

Solving Inequalities one-step and multi-step inequalities –follow the steps for solving an equation –reverse the inequality symbol when multiplying/dividing by a negative number compound inequalities –rewrite as two separate inequalities, if necessary absolute value inequalities –isolate the absolute value expression on one side of the inequality –rewrite as a compound inequality, then solve

Example Graph the inequality:x > 3

Example Graph the inequality:x ≤ -2

Example Solve, then graph your solution: x – 5 > -3.5

Example Solve, then graph your solution: x – 9 ≤ 3

Example 3x – 7 < 8

Example -0.6 (x – 5) ≤ 15

Example 2x – 5 ≤ 23

Example -6y + 5 ≤ -16

Example - ¼ (p – 12) > -2

Example 6x – 7 > 2x + 17

Example 14x + 5 < 7 (2x – 3)

Example 12x – 1 > 6 (2x – 1)

Example 2 < x + 5 < 9

Example -5 ≤ -x – 3 ≤ 2

Example 2x

Example 4c + 1 ≤ -3 or 5c – 3 > 17

Example |x| = 7

Example |x - 3| = 8

Example 3 |2x - 7| - 5 = 4

Example 4 |t + 9| - 5 = 19

Solving Absolute Value Inequalities when you have: less than (< or ≤):we write it as a “sandwich” |x + 1|< 3 -3 < x + 1 < 3 greater than (> or ≥): we write it as an “or” |x + 1| > 3 x + 1 > 3 or x + 1 < -3 Remember as: –less “and” –great “or”

Solving Absolute Value Inequalities Isolate the absolute value first –(get it by itself) make it an “and” or an “or” statement solve and graph

Example |x| ≥ 6

Example |x| ≤ 0.5

Example |x - 5| ≥ 7

Example |-4x - 5| + 3 < 9

Example 3|5m - 6| - 8 ≤ 13

Graphing Linear Inequalities step 1:graph the boundary line, as we would with any other line –if the inequality is >/<, use a dotted line –if the inequality is ≤/≥, use a solid line step 2:shade –above the line if >/≥ –below the line if </≤

Example y > 4x - 3

Example x + 2y ≤ 0

Example x + 3y ≥ -1

Example y ≥ -3

Example x < -1

Graphing Systems of Inequalities graph each inequality, shading as required find the intersection of the shaded areas the common solution of the system is the common shaded area colored pencils help tremendously!!!

Example y > -x – 2 y ≤ 3x + 6

Example y ≥ -1 x > -2 x + 2y ≤ 4

Example y < x – 4 y ≥ -x + 3

Example y ≥ -x + 2 y < 4 x < 3