1st 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

ExampleExample

3x – 7 < 83x – 7 < 8

ExampleExample

-0.6 (x – 5) ≤ 15-0.6 (x – 5) ≤ 15

ExampleExample

2x – 5 ≤ 232x – 5 ≤ 23

ExampleExample

-6y + 5 ≤ -16-6y + 5 ≤ -16

ExampleExample

- ¼ (p – 12) > -2- ¼ (p – 12) > -2

ExampleExample

6x – 7 > 2x + 176x – 7 > 2x + 17

ExampleExample

14x + 5 < 7 (2x – 3)14x + 5 < 7 (2x – 3)

ExampleExample

12x – 1 > 6 (2x – 1)12x – 1 > 6 (2x – 1)

Example

2 < x + 5 < 9

Example

-5 ≤ -x – 3 ≤ 2

Example

2x + 3 < 9 or 3x – 6 > 12

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