Section 2 8 Inequalities and Their Graphs pages

• An inequality is a mathematical sentence that contains >, <, ≥, ≤,

Graphing Solutions of Inequalities a) x > -2 An open dot shows that –

Graphing Solutions of Inequalities b) w ≥ -5 A closed dot shows that –

Graphing Solutions of Inequalities c) k ≤ 4 A closed dot shows that 4

Graphing Solutions of Inequalities d) y < 6 An open dot shows that 6

Check Understanding Graph the solution of each inequality. a) z < -2 b) 4>x

Writing Inequalities to Describe Graphs Write the inequality shown in each graph. a) b)

Writing Inequalities Food can be labeled very low sodium only if it meets the

Words A serving of very low sodium 35 mg sodium number of milligrams of

Check Understanding Use the table in Example 3. A certain food is labeled sodium

Homework: • pages 104 – 105, #s 2 -12 even, 13 -16, 2026 even,

Slides: 12

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Section 2 -8 Inequalities and Their Graphs pages 102 -105 • Graph Inequalities • Write Inequalities

• An inequality is a mathematical sentence that contains >, <, ≥, ≤, or ≠. • Some inequalities contain a variable. • Any number that makes an inequality true is a solution of the inequality. • For example, -4 is a solution of y ≥ -5 because -4 ≥ -5.

Graphing Solutions of Inequalities a) x > -2 An open dot shows that – 2 is not a solution. Shade all points to the right of -2.

Graphing Solutions of Inequalities b) w ≥ -5 A closed dot shows that – 5 is a solution. Shade all points to the right of -5.

Graphing Solutions of Inequalities c) k ≤ 4 A closed dot shows that 4 is a solution. Shade all points to the left of 4.

Graphing Solutions of Inequalities d) y < 6 An open dot shows that 6 is not a solution. Shade all points to the left of 6.

Check Understanding Graph the solution of each inequality. a) z < -2 b) 4>x c) a ≤ -5 d) 2≥c

Writing Inequalities to Describe Graphs Write the inequality shown in each graph. a) b)

Writing Inequalities Food can be labeled very low sodium only if it meets the requirements established by the federal government. Use the table to write an inequality for this requirement. Label Sodium-free food Definition Less than 5 mg per serving Very low sodium food At most 35 mg per serving Low-sodium food At most 140 mg per serving

Words A serving of very low sodium 35 mg sodium number of milligrams of sodium in a = serving of very low sodium food. Let v Equation Has at most v ≤ 35

Check Understanding Use the table in Example 3. A certain food is labeled sodium free. Write an inequality for n, the number of milligrams of sodium in a serving of this sodium free food.

Homework: • pages 104 – 105, #s 2 -12 even, 13 -16, 2026 even, 27, 28, 37, 39 -41 • You are expected to write the problems (except for word problems and multiple choice problems) • and show all of your work on every problem. • Failure to write the problems/show the work will result in either receiving partial or no credit.