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 < -1 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 < 5 or 4x – 7 >9

Solving an “OR” compound inequality

You do: 6x + 9 < 3 or 3x – 8 > 13

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 or ax + b > c

Greator than

Solving an Absolute Value Inequality of the form: |ax + b| > c

You do: |-x + 1| > 15

ax + b < -c or ax + b > c

Solving an Absolute Value Inequality of the form: |ax + b| > c

You do: 3|-2x| > 15

ax + b < -c or ax + b > c