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