Solving Linear Inequalities Remember…. “I’m bigger than you are….” > OR “The alligator eats the bigger number….” <

Solving an inequality with a variable on one side 5y – 8 < 12

You do: 11y – 9 > 13 Solving an inequality with a variable on one side

2x + 1 < 6x - 1 Solving an inequality with a variable on both sides

You do: 7x + 9 > 10 x -12 Solving an inequality with a variable on both sides

-2 < x < 1 A COMPOUND INEQUALITY is two simple inequalities joined by “and” or “or”. x 2 All real numbers that are greater than or equal to -2 AND less than 1. All real numbers that are less than -1 OR greater than or equal to 2

Solving an “AND” compound inequality -2 < 3t – 8 < 10

Solving an “AND” compound inequality You do: -9 < y + 4 < 10

Solving an “OR” compound inequality 2x + 3 9

Solving an “OR” compound inequality You do: 6x

Solving Linear Inequalities Remember…. “I’m bigger than you are….” > OR “The alligator eats the bigger number….” <

Solving an Absolute Value Equation The absolute value of a number |x| is the distance the number is from 0 on a number line. |x| = 5 |2x - 5| = 9

Solving an Absolute Value Equation You do: |6x - 3| = 15

Solving an Absolute Value Equation 2|3x - 3|+ 5 = 13

Solving an Absolute Value Equation You do: -|3x + 8|-6 = 15

Solving an Absolute Value Inequality of the form: |ax + b| < c |2x + 7| < 11 Less thand -c < |ax + b| < c

Solving an Absolute Value Inequality of the form: |ax + b| < c You do: |4x - 9| < 21 -c < |ax + b| < c

Solving an Absolute Value Inequality of the form: |ax + b| < c You do: 2|x - 5| - 8 < 20 -c < |ax + b| < c

Solving an Absolute Value Inequality of the form: |ax + b| > c |3x - 2| > 8 ax + b c Greator than

Solving an Absolute Value Inequality of the form: |ax + b| > c You do: |-x + 1| > 15 ax + b c

Solving an Absolute Value Inequality of the form: |ax + b| > c You do: 3|-2x| > 15 ax + b c