Problem of the Day The hypotenuse of a right triangle is 2 cm longer than one leg. It is 4 cm longer than the other leg. How long is the hypotenuse?

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Presentation transcript:

Problem of the Day The hypotenuse of a right triangle is 2 cm longer than one leg. It is 4 cm longer than the other leg. How long is the hypotenuse?

One-Variable Equations and Inequalities Chapter 2 Section 2.4

Equations and Inequalities Any value of the variable that makes an equation or an inequality true is a solution. Solving an inequality is similar to solving an equation. Solutions to inequalities using one variable can be graphed on a number line. The bottom of page 75 illustrates these examples.

Equations and Inequalities 4. Graph each equation or inequality. a. x > -7 b. x ≠ 5 c. 4 < x < 10

Equations and Inequalities Example 1 Solve 6x + 2(3 – x) = 7x + 1.

Equations and Inequalities 5.Solve each equation. Check each answer. a. 3x + 1 = 16 b. 10x + 4 = 8 – 2x c. 2(x – 3) = 4x d. 4x – 5(x – 2) = 9x – 14

Equations and Inequalities Example 2 Jeanine has $20 and is going shopping to buy three scarves and as many pairs of earrings as possible. How many pairs of earrings can she buy?

Equations and Inequalities 6.Solve 5x – 3(x + 4) > 10. An absolute value equation such as |x – 6| = 10 has two solutions, since the expression x – 6 can equal 10 or -10.

Equations and Inequalities Example 3 Solve and graph the equation |x – 6| = 10.

Interpreting Linear Functions 7. Solve and graph each equation. a. |x| – 5 = 7 b. |x + 5| = 7c. |x – 7| = 5

Equations and Inequalities You can solve simple absolute value inequalities by graphing the solutions. (See the top of page 78 in the textbook) Sometimes you need to rewrite an absolute value inequality as two inequalities. Then you can solve each inequality algebraically.

Equations and Inequalities Example 4 Solve each inequality. Graph the solutions on a number line. a. |x + 4| 5

Equations and Inequalities 9. Solve each inequality. Graph the solutions on a number line. b. 2|x + 8| 5

Assignment Pgs (1-45 odd)