Martin-Gay, Beginning Algebra, 5ed 22

33 Add 10 to both sides Subtract 5 from both sides Multiple both sides by 2 Multiple both sides by  2 Divide both sides by 3 Divide both sides by  3

Martin-Gay, Beginning Algebra, 5ed 44 Example: Solve the inequality, and graph the solution. 2(x – 3) < 4x x – 6 < 4x + 10 Distribute. – 2x – 6 < 10 Subtract 4x from both sides. – 2x < 16 Add 6 from both sides. x > – 8 Divide both sides by  2, switch inequality.  8 0 x

Martin-Gay, Beginning Algebra, 5ed 55 Interval notation, is used to write the numerical solution for inequalities. Use a bracket if you want to include the number Use a parenthesis if you DO NOT want to include the number. 0 0 Numerical Notation call “Interval Notation”: x x x  7 x >  4

Martin-Gay, Beginning Algebra, 5ed 66 x < 3 –5  x means x > –5 Interval notation: (–∞, 3) Interval notation: [–5, ∞) Included NOT included 03 x 55 0 x

Martin-Gay, Beginning Algebra, 5ed 77 0 x

88 Since 0 is always greater than –7, the solution is all real numbers. (Any value we put in for x in the original statement will give us a true inequality.) Example: Solve the inequality. Graph the solution and give your answer in interval notation. x + 5  x – 2 x  x – 7 Subtract 5 from both sides. 0  – 7 Subtract x from both sides. (Always true!) (–∞, ∞) 0 x

Martin-Gay, Beginning Algebra, 5ed x

10 3x + 9  5(x – 1) 3x + 9  5x – 5 Use distributive property on right side. 3x – 3x + 9  5x – 3x – 5 Subtract 3x from both sides. 9  2x – 5 Simplify both sides. 14  2x Simplify both sides. 7  x Divide both sides by  2x – Add 5 to both sides. Example: Solve the inequality. Graph and write in interval form. x < 7 (–∞, 7] 0 x 7