BELLWORK Eureka Module 1 Lesson 15 Exercise 4

BELL-WORK *Eureka Module 1 Lesson 15 Exercise 4, f, g * Solve and graph the solutions of: 8 ≤ 2 y + 4 ≤ -6(y – 2) + 48 8 ≤ 2 y + 4 y≥ 2 and 2≤y≤ 7 2 y + 4 ≤ -6(y – 2) + 48 y≤ 7

Compound Inequalities To earn a B in your Algebra course, you must achieve an unrounded test average between 84 and 86, inclusive. You score 86, 85, and 80 on the first three tests of the grading period. What possible scores can you earn on the fourth test to earn a B in the course? 84 ≤ 86 + 85 + 80 + x ≤ 86 4 336 ≤ 251 + x ≤ 344 85 ≤ x ≤ 93

Compound Inequalities When two inequalities are joined by the word ‘or’ a disjunction is formed. Ex. All real numbers that are less than 0 or greater than 3. So, x < 0 or x > 3

Compound Inequalities When two inequalities are joined by the word ‘or’ a disjunction is formed. Ex. All real numbers that are less than 0 or greater than 3. So, x < 0 or x > 3 Which is graphed as:

Compound Inequalities When two inequalities are joined by the word ‘or’ a disjunction is formed. Ex. All real numbers that are less than 0 or greater than 3. So, x < 0 or x > 3 Notice there is a gap in the graph, which implies that solutions to disjunctions make only one of the components true.

Compound Inequalities Write a compound inequality to represent all real numbers that are less than or equal to 2½ or greater than 6. x ≤ 2½ or x > 6

Solving Disjunctions Solve and graph 3 x + 2 < -7 OR -4 x + 5 < 1 When solving disjunctions, simply solve each inequality separately. 3 x + 2 < -7 3 x < -9 x < -3 OR OR -4 x + 5 < 1 -4 x < -4 x>1

Solving Disjunctions Solve and graph 3 x + 2 < -7 OR -4 x + 5 < 1 When solving disjunctions, simply solve each inequality separately. 3 x + 2 < -7 3 x < -9 x < -3 OR OR -4 x + 5 < 1 -4 x < -4 x>1

Solving Disjunctions What are the solutions of -2 y + 7 < 1 or 4 y + 3 ≤ -5? Graph the solutions. -2 y + 7 < 1 -2 y < -6 y>3 or 4 y + 3 ≤ -5 4 y ≤ -8 y ≤ -2