Keystone Review inequalities

A1.1.3.1.1 Write/solve compound inequalities and/or graph their solution sets on a number line (may include absolute value inequalities). When graphing: < or > use an open circle and/or dashed line ≤ or ≥ use a closed circle and/or solid line Example 1: Solve and graph the compound inequality 3<4𝑥−5<11

Example 2: Solve and graph the compound inequality 6<−2𝑥+2<10

Example 3: Solve and graph the compound inequality 4+𝑥<−6 𝑜𝑟 10𝑟>0

On your own: Solve and graph the compound inequality 5<2−3𝑥<14

Example 3: A1.1.3.1.2 Identify or graph the solution set to a linear inequality on a number line Single variable problems: Given: Which inequality represents the graph above: a) 3x + 13 < -5 b) 3x + 13 > -5 c) 3x + 13 ≥ -5 d) 3x + 13 ≤ -5

On your own: Single variable problems: Given: Which inequality represents the graph above: a) 2x + 5 < -1 b) 2x + 5 ≤ -1 c) 2x + 5 > -1 d) 2x + 5 ≥ -1

Example 4: A1.1.3.2.1 Solve a system a linear inequalities with graphing Graph the system of inequalities. 𝑦<𝑥−6 𝑦>2𝑥

Example 5: Graph the systems of inequalities 𝑦−2𝑥>1 𝑦−3𝑥<3

On your own: Graph the systems of inequalities 𝑦≥− 1 2 𝑥+3 𝑦<2𝑥−1

Example 6: Tyreke always leaves a tip of between 8% and 20% for the server when he pays for his dinner. This can be represented by the system of inequalities shown below, where y is the amount of tip and x is the cost of dinner. 𝑦 > 0.08𝑥 𝑦 < 0.2𝑥 Which of the following is a true statement? A. When the cost of dinner, x, is $10, the amount of tip, y, must be between $2 and $8. B. When the cost of dinner, x, is $15, the amount of tip, y, must be between $1.20 and $3.00. C. When the amount of tip, y, is $3, the cost of dinner, x, must be between $11 and $23. D. When the amount of tip, y, is $2.40, the cost of dinner, x, must be between $3 and $6.

On your own: (think pair share) A baseball team had $1,000 to spend on supplies. The team spent $185 on a new bat. New baseballs cost $4 each. The inequality 185 + 4b 1,000 can be used to determine the number of new baseballs (b) that the team can purchase. Which statement about the number of new baseballs that can be purchased is true? A. The team can purchase 204 new baseballs. B. The minimum number of new baseballs that can be purchased is 185. C. The maximum number of new baseballs that can be purchased is 185. D. The team can purchase 185 new baseballs, but this number is neither the maximum nor the minimum.

Example 7: A1.1.3.1.3 Interpret solutions to linear inequalities in the context of the situation An online game service charges $12 per month and $1.50 for each game played. Last month you spent $42 more than you earned and had to borrow the money from your parents to pay the bill. This month you have to pay back your parents before you can play the game. If you work 5 hrs a week at a rate of $7.50 an hour (disregard taxes). How many hours will you be able to play the game this month? How many games did you play last month? X = the number of games you can play this month Earnings: 4×5×$7.5=150 42+12+1.5𝑥≤150 54+1.5𝑥≤150 1.5𝑥≤96 𝑥≤64 $138/$1.5=92 games per month therefore he played 92+(42/$1.50)=120 games last month

Example 8: A1.1.3.2.2 Interpret solutions to systems of linear inequalities in context Laura purchased vegetables from a supermarket. She spends not more than $30 for potatoes (x) and onions (y). Potatoes cost $1/lb and onions cost $2/lb. She needs at least 18 pounds combined. Which of the following is a possible combination for the number of pounds of each Laura purchased. Write a system of inequalities Solve systems for y a) (17, 0) b) (24, 2) c) (2, 24) d) (0, 17)