Solving Inequalities:

Text Box: KEY IDEAS:
· Use the same rules as you would in solving equations
· When multiplying or dividing both sides of the inequality by a negative number, the inequality is reversed.

Text Box: Steps:
· Expand to remove brackets
· Collect like terms on each side of equation
· Reverse inequality when dividing both sides by “-2”
· Graph has closed dot at x = -3 to show –3 is included as well as all points to the left of -3

$Text Box: Steps: · Remove fractions by multiplying each term by the LCD which is 4 · Collect like terms on each side of equation · Reverse inequality when dividing both sides by –8 · Graph has open dot at x = 7/8 to show 7/8 is not included · Include all points to the right of x = 7/8, but not x = 7/8$

$Text Box: Steps: · Add 3 to each part of the inequality · Multiply each part by 3 to remove fractions · Graph has closed dot at 3 and open dot at 12 · Include all points between these limits$

Absolute value:

Intuitively, the absolute value of a number a denoted | a | is it’s distance from the origin or it’s magnitude without regard to sign. Hence the absolute value of a number will always be a positive number or zero.

Examples:

Equations Involving Absolute Value:

Inequalities Involving Absolute Value:

Text Box: Absolute Value Inequalities:

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