Solving Linear Inequalities and Compound Inequalities

Inequality Symbols is less than is greater than is less than or equal to is greater than or equal to is not equal to

Linear Inequality Can be written in the form ax+b 0, ax+b≤0, or ax+b≥0 where a and b are real numbers and a≠0 Has one variable to the first power. for example: 2x-3<8 A solution is a value of the variable that makes the inequality true. x could equal -3, 0, 1, etc.

Transformations for Inequalities Add/subtract the same number on each side of an inequality Multiply/divide by the same positive number on each side of an inequality If you multiply or divide by a negative number, you MUST flip the inequality sign!

Ex: Solve the inequality. 2x-3< x<11 2 x< Flip the sign after dividing by the -3!

Graphing Linear Inequalities Remember: signs will have an open circle and signs will have a closed circle graph of

Example: Solve and graph the solution. 6789

This is a true statement, therefore the solution is ALL REAL NUMBERS.

Compound Inequality An inequality joined by “and” or “or”. Examples “and”/intersection “or”/union think between think oars on a boat

Example: Solve & graph. -9 < t+4 < < t < 6 Think between! -136

Solve & graph. -6x x 21 x > 1 or x < -7 Flip signs Think oars -71

Assignment Assignment p #12-33 m3, 42, 48, 51, 53, 56 Assignment