2.5 Solving Compound Inequalities

Conjunctions- use the word “and” x > 5 and x < 10 for the solution to x both statements must be true a sentence like this means that x has to be larger than 5, but has to be 10 or less Remember the line and closed points represent all possible solutions. The graph…

More Examples x > -2 and x < 1 x has to be -2 or greater, but less than 1 -3 < x < 6 This is an abbreviated form of saying x has to be greater than -3, but less than 6

Try this… a.) -3 < x and x < 4 b.) -7 < x < -3

Solve and Graph -6 < 2x + 4 < 10 -4 - 4 -4 -10 < 2x < 6 2 2 2 -5 < x < 3

Graph the conjunction. -5 < x < 3

Try this… c.) -18 < 3x – 6 < -3 -18 < 3x – 6 < -3 +6 +6 +6 +6 +6 +6 -12 < 3x < 3 3 3 3 -4 < x < 1

Disjunctions- use the word “or” x < -3 or x > 6 One or both statements must be true The graph…

Solve and graph -3x – 4 > 8 or x – 6 > 1 +4 +4 -3x > 12 -3 -3 x < -4 x – 6 > 1 +6 +6 x > 7

Try this… d.) -2x – 6 > 4 or x + 5 > 8 x < -5 or x > 3