Math Journal 10-13 𝑥−17=25 2. 𝑥 13 −12=15 3. 5𝑥=25 4. −14𝑥+5+2𝑥=−4𝑥−3 Solve for x. 𝑥−17=25 2. 𝑥 13 −12=15 3. 5𝑥=25 4. −14𝑥+5+2𝑥=−4𝑥−3 Math Journal 10-13

Unit 3 Day 5: Solving One and Two Step Linear Inequalities Essential Questions: How do we graph linear inequalities in one variable? How do we solve one and two step linear inequalities?

Vocabulary < "𝑙𝑒𝑠𝑠 𝑡ℎ𝑎𝑛“ ≤ "𝑙𝑒𝑠𝑠 𝑡ℎ𝑎𝑛 𝑜𝑟 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜" Inequality Signs (as read from left to right ) < "𝑙𝑒𝑠𝑠 𝑡ℎ𝑎𝑛“ ≤ "𝑙𝑒𝑠𝑠 𝑡ℎ𝑎𝑛 𝑜𝑟 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜" > "𝑔𝑟𝑒𝑎𝑡𝑒𝑟 𝑡ℎ𝑎𝑛" ≥ "𝑔𝑟𝑒𝑎𝑡𝑒𝑟 𝑡ℎ𝑎𝑛 𝑜𝑟 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜" Graph of the Inequality: the set of points on a number line that represent all solutions of the inequality.

Graphing Linear Inequalities When graphing inequalities use an: open dot for < and > close dot for ≤ and ≥ Draw a ray in the direction of the inequality sign. Verbal Phrase: Graph : All real numbers less than 2 1 2 3 -1 -2 x < 2 All real numbers greater than -2 x > -2 1 2 3 -1 -2 All real numbers less than or equal to 1 1 2 3 -1 -2 x < 1 All real numbers greater than or equal to 0 x > 0 1 2 3 -1 -2

s > 73 x ≥ -9 x ≤ 10 Example 1: Graph the inequality. Sarah was sure that she scored at least a 73% on her algebra test. Write and graph an inequality for Sarah’s possible test scores. -7 1 x ≥ -9 x ≤ 10 -9 10 s > 73 73

Solving Linear Inequalities When solving linear inequalities, treat each problem the same as when you solve a regular equation. ***THE ONLY DIFFERENCE***: when you multiply or divide by a negative number, you MUST flip the inequality symbol! < changes to > > changes to <

a) x + 5 > 5 b) -2 > n - 4 Example 2: Solve the inequality. - 5 + 4 + 4 2 > n x > 0 n < 2 c) 5x > -45 d) < 12 a -3 (-3) (-3) 5 5 x > -9 x > -36

Example 3: Solve the inequality. 2x + 4 > 24 -b - 2 > 8 - 4 - 4 + 2 + 2 2x > 20 -b > 10 2 2 -1 -1 x > 10 b < -10 4 + < 6 - 6 < -6 m -4 n 3 - 4 - 4 + 6 + 6 n 3 < 2 m -4 < 0 (3) (3) (-4) (-4) n < 6 m > 0

Example 4: Medical Problem A nurse wants to give a patient medicine. She wants to give the patient the same dosage every 6 hours, but he cannot exceed 32 ml in a day. What is the maximum dosage that the nurse can give the patient each time? If the patient receives a dosage every 6 hours, then how many dosages will the patient get in one day? 4 dosages 4d < 32 4 4 d < 8 Each dosage can be a maximum of 8ml.

Summary Essential Questions: How do we graph linear inequalities in one variable? How do we solve one and two step linear inequalities? Take 1 minute to write 2 sentences answering the essential questions.