Solving and Graphing Inequalities

Chapter 6Solving and Graphing InequalitiesRules for graphing your answersIf the letter is on the left then we can follow the direction of the arrowWe must mark the numbers< or > we use an open circle< or > we use a closed circle

Our answers will look like this and we will graph the answers on a number lineX < 2X > -2Z > 10 < dNow you practice:T > 1X >-1N < 04 >yOur problems will look like this:X + 5 > 3We will use our Chapter 3 rules to solve:Draw tracksCount variablesIf one, numbers jump tracksIf 2 or more where are theySame side, family membersDifferent sides, letters jumpAdd or subtract the numbersIs there a number on the letters? If its an integer divide each sideIf its a fraction, flip and multiplyif the integer or fraction is negative I must turn the arrow around to the opposite directionGraph the solution

More examples:X + 4 < 7N + 6 > 25 > a + 5-2 > n 4X 5 > 2P 1 < -4-3 < y - 2Pg 327 #s 42 54 evenSec 6.2Solving Equations using Multi or DivWe must be able to identify if there is an integer on the letter or a fraction on the letter.If the integer or the fraction is negative then we MUST change the direction of the arrow in our answerExamplesa/4 < 44x > 20k/4 < 18 < 2k6 < t/5-21 < 3yExamples: Negative numbers-1/2 y < 5-12m > 18-8x < 20-1/5 p > 1-2/3 x < -5-24 < 6tWord ProblemsKayla wants to buy some posters for her dorm room. Posters are on sale for $6 each. Write and solve an inequality to determine how many posters she can buy and spend no more than $25.Crandell plans to take figure skating lessons. He can rent skates for $5 per lesson. He can buy skates for $75. For what number of lessons is it cheaper for him to buy rather than rent skates?Pg 334 #s 36 46 evenQuizSections 6.1 and 6.2X 4 < -5-11 > y + 4-1/2 x > -5-3x < -27-3/4 x < -1/4Sec 6.3; Solving Multi-step Inequalities2y 5 < 75 x > 43(x + 2) < 7-2(x + 1) < 22x 3 > 4x 1Sec 6.3; Solving Multi-step Inequalities5n 21 < 8n-3z + 15 > 2z X + 3 > 2x 4 4y 3 < -y + 12

Word ProblemsYou plan to make and sell candles. You pay $12 for instructions. The materials for each candle cost $0.50. You plan to sell each candle for $2. Let x be the numbers of candles you sell. How many candles must be sold to make at least $300 profit.Sec 6.4; Solving compound inequalitiesHow do you combine two thoughts in English class?What are they called?What words do we use?How to Solve:-2 < x + 2 < 4-1 < x + 3 < 7-6 < -3x < 120 < x 4 < 12These are AND problems. These problems must be re-written into two problems. Word ProblemsIn the summer it took a Pony Express rider about 10 days to ride from St. Joseph, Missouri to Sacramento, California. In winter it took as many as 16 days. Write an inequality to describe the number of days that the trip might have taken.Word ProblemsFrequency is used to describe the pitch of a sound. Frequencies are measured in hertz. Write an inequality for the followingSound of a human voice: 85 hertz to 1100 hertzSound of a bats signal: 10,000 hertz to 120,000 hertzSound heard by a dog: 15 hertz to 50,000 hertzSound heard by a dolphin: 150 hertz to 150,000 hertzPg 346 #s 30-46 evenSec 6.5; Solving Compound InequalitiesThese are called OR problemsThese problems are already written and ready to be solvedExamplesX-4 183x + 1 < 4 or 2x 5 > 7X + 5 < -6 or 3x > 126x 5 < 7 or 8x + 1 > 25Word ProblemA baseball is hit straight up in the air. Its initial velocity is 64 ft per second. Its formula is v = -32t + 64. Find the values of t for which the velocity of the baseball is greater than 32 or less than -32 feet per second.Sec 6.6; Absolute Value EquationsThese problems will create some re-writing1st make sure the absolute value bars are on a side by themselves2nd drop the bars and write two problems3rd in the second problem you will need the opposite of the symbol (equals or inequality) and the opposite of the number.Now solve the equationsIf its an inequality then you will also graph the solutions.For examples we will use p. 356Pg. 358 #s 16-26 evenpg 359 #s 32-40 evenSec 6.7; Solving absolute value inequalitiesWe will use the same rules as the previous section (6.6)Make sure to remember to make the changes to the second problem that you re-write.We will use pg 364 and 365 for examplesSec 6.8; Graphing Linear Inequalities in Two VariablesWe use our previous knowledge from Chapters 4 and 5.To graph we will use y= mx + bSlope intercept form: y = mx + bb is the y-intercept. I must always use this number first when graphing. It is always located on the y-axis, either above or below the origin. m is the slope. Its always a fraction and remember to use rise over run

To graph given when given an equation; turn it into y=mx+bIf the symbol is < or > we will draw a dashed lineIf the symbol is < or > we will draw a normal lineTo shade will have to use a test point and the slope intercept formIf the test result is false shade away from the TP, if the test is true shade to the TP.Flow ChartLet x jump the tracksIf there is a number on y, then we will set up three fractions and divide or reduceCollect b and find it on the y-axisCollect m and use rise over run to get to the next point on my line.-2x + y < 3

MORE EXAMPLES:X < -2Y < 1X + Y > 32X Y > -23X Y < 4P 371 #S 26-30 EVENP 371 #S 36-50 EVEN