5-1 Solving Linear Inequalities by addition and Subtraction Goals: Graph linear inequalities on a number line. Solve linear inequalities by adding and subtracting. Using linear inequalities to solve real life problems. Eligible Content: A1.1.3.1.2 / A1.1.3.1.3

Vocabulary Inequality – any problem containing <, >, ≤ or ≥. Graph – all numbers on a number line that will work in the inequality. Solve – get the variable alone.

Graphing a Linear inequality Graph: x < 2 x ≤ -2 x > - 4 x ≥ 3

Summary < and >  draw an open circle: ≤ and ≥  draw a closed circle: Shade in the direction the inequality symbol points. < and ≤  shade left > and ≥  shade right

Examples Graph each inequality: x < 6 x ≥ -4 4 < x x ≤ -2

Solve the inequality (same as before) x + 7 < 12 - 7 - 7 x < 5 x - 2 ≥ 15 +2 +2 x ≥ 17

Examples Solve each linear inequality: x + 3 < 4 x – 9 ≥ 4 x < 1 x ≥ 13 x > 3 x < -18 x > 6

Solve k – 4 < 10. A. k > 14 B. k < 14 C. k < 6 D. k > 6

Solve the inequality m – 4  –8. A. m  4 B. m  –12 C. m  –4 D. m  –8

Solve 3p – 6 ≥ 4p. Graph the solution. B. p ≤ –6 C. p ≥ –6 D. p ≥ –6

Practice Page 288 #1-8

Word Problem #1 Megan wants to buy season passes to two theme parks. If one season pass costs $54.99 and Megan has $100 to spend on both passes, the second season pass must cost no more than what amount? 54.99 + x ≤ 100 x ≤ 45.01 Less than $45.01

Word Problem #2 Jeremy is taking two of his friends out for pancakes. If he spends $17.55 on their meals and has $26 to spend in total, Jeremy’s pancakes must cost no more than what amount? 17.55 + x ≤ 26 x ≤ 8.45 Less than $8.45

Word Problem #3 The temperature for a lizard cage has to be at least 82°F. Currently the temperature is 62.5°F. How much warmer does the cage need to be? 62.5 + x ≥ 82 x ≥ 19.5 At least 19.5°F warmer

Homework Pages 288-289 #12-28 even #34-39 all