Winter, 2010-2011. CH4-1 Inequalities and Their Graphs Background: Many times we don’t know the...

Winter, 2010-2011

CH4-1 Inequalities and Their GraphsBackground: Many times we don’t know the

answer but we certainly know what range we need or want. For example, nurses want to see body temperatures of what? Nurses might look body temperatures to be LESS than or equal to 98.6 °F. Speed limits allow us to drive LESS than 70 mph but GREATER than 45 mph.

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CH4-1 Inequalities and Their GraphsVocabulary for SYMBOLS:

< means….LESS THAN (mouth closed to smaller quantity)> means…..GREATER THAN (mouth opens to bigger quantity)≤ means….LESS THAN OR EQUAL TO (mouth closed to smaller qty)≥ means….GREATER THAN OR EQUAL TO (mouth opens to bigger qty)

① means…The number 1 is NOT INCLUDED

❶ means….The number 1 IS INCLUDED

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CH4-1 Inequalities and Their GraphsHow To Use It:

Ex.1 Determine whether each number is a solution of the given inequality.

-1 > x a. 0 b. -3 c. -6a. -1>0 Is this true?NO!b. -1>-3Is this true?YES!c. -1 > -6YES!

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CH4-1 Inequalities and Their GraphsWhen in doubt, put it on the number line and

doublecheck!

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CH4-1 Inequalities and Their Graphs

Now, you do ODDS,

1-27

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4-2 & 4-3 Solving InequalitiesSo, how do you solve inequalities? Same as you did with = sign in CH3!! ALWAYS FOLLOW YOUR RECIPE!!!!

Recipe to Solve EquationsStep1: Get x term(s) alone on one side =

sign.Step2: Combine Like Terms.Step3: Isolate x using opposite functions.Step4: Plug x value back in to original

question and check answer.7

4-2 & 4-3 Solving Inequalities How To Use It: Ex.1 Solve each inequality. Check your solution.n – 7 ≥ 2 +7 +7n ≥ 9

9 – 7≥ 22 ≥2

Recipe to Solve EquationsStep1: Get x term(s) alone on one side

of = sign.Step2: Combine Like Terms.Step3: Isolate x using opposite

functions.Step4: Plug x value back in to original

question and check answer.

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4-2 & 4-3 Solving Inequalities How To Use It: Ex.2 Solve each inequality. Check your solution.a ≤ -141a ≤ -14

0.25a ≤ -10.25 0.25a ≤ -4

Recipe to Solve EquationsStep1: Get x term(s) alone on one side

of = sign.Step2: Combine Like Terms.Step3: Isolate x using opposite

functions.Step4: Plug x value back in to original

question and check answer.

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CH4-2 & 4-3 Solving Inequalities

Now, you do:4-2: Evens 2-20, 22, 24 4-3: ODDS, 1-23

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CH4-4 Solving Multi-Step InequalitiesWhat if there are variables on both sides of the inequality

sign? What do we do then?Same as CH3! Use the recipe to solve for the variable.

Recipe to Solve EquationsStep1: Get x term(s) alone on one side

of = sign.Step2: Combine Like Terms.Step3: Isolate x using opposite

functions.Step4: Plug x value back in to original

question and check answer. 11

CH4-4 Solving Multi-Step InequalitiesHow To Use It: Ex.1 Solve each

inequality. 2(3+3g) ≥ 2g + 14PEMDAS starts it off…6 + 6g ≥ 2g + 14 -2g ≥ -2g 6 + 4g ≥ +14-6 ≥ -6 +4g ≥ +8 4 4

g ≥ 2

Recipe to Solve Equations

Step1: Get x term(s) alone on one side of = sign.

Step2: Combine Like Terms.

Step3: Isolate x using opposite functions.

Step4: Plug x value back in to original question and check answer.

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CH4-4 Solving Multi-Step InequalitiesHow To Use It: Ex.2 Write and solve an inequality that models each

situation. Suppose it costs $5 to enter a carnival. Each ride costs

$1.25. You have $15 to spend at the carnival. What is the greatest number of rides that you can do?

First, define variable(s):r= number of rides$5 = entry fee (to be added to cost of rides)$15 = total cost Next, start writing sentences as math equationTotal cost = entry fee + cost of rides

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CH4-4 Solving Multi-Step InequalitiesHow To Use It: Ex.2 Write and solve an inequality that models each

situation. Suppose it costs $5 to enter a carnival. Each ride costs

$1.25. You have $15 to spend at the carnival. What is the greatest number of rides that you can do?

Next, plug-in what you know into this equation.Total cost = entry fee + cost of rides$15 = $5 + $1.25 r∙

But now, look at the = sign is that right? No, we know the MAX we can spend is $15 so the right side

of that equation better be LESS THAN or EQUAL TO THAT14

CH4-4 Solving Multi-Step InequalitiesHow To Use It:Suppose it costs $5 to enter a carnival. Each ride costs

$1.25. You have $15 to spend at the carnival. What is the greatest number of rides that you can do?

So, what sign do we use?≥$15 ≥ $5 + $1.25 r∙-5 ≥ -510 ≥ 1.25 r∙1.25 ≥ 1.258 ≥ rYou can buy NO MORE THAN 8 RIDES

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CH4-4 Solving Multi-Step Inequalities

Now, you do:Evens 2-20

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CH4-5 Compound InequalitiesBackground:Sometimes, we want a range for the answer, not just one

value. What do we do when this happens? How do we solve something like:

-4 < t+2 < 4Nothing is different than before! You still want to isolate

your variable, using your recipe….

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CH4-5 Compound InequalitiesHow To Use It: Ex.1 Solve each inequality. -4 < t+2 < 4 Steps 1-3 are done-4 < t+2 < 4-2 -2 -2-6 < t < 2Graph it on a number line to

see if this result makes sense

Recipe to Solve Equations

Step1: Get x term(s) alone on one side of = sign.

Step2: Combine Like Terms.

Step3: Isolate x using opposite functions.

Step4: Plug x value back in to original question and check answer.

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CH4-5 Compound Inequalities

Now, you do:Odds 1-15

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CH4-6 Absolute Value Equations and InequalitiesBackground:When you have absolute value bars, you have two possible

solutions, a positive and a negative.Ex.1 |x| = 6

x can be +6x can also be -6

So you have to switch the = sign for an inequality and make the number negative, to get answers. So it is easiest to just write two equations and solve for the two answers.

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CH4-5 Compound InequalitiesHow To Use It: Ex.2 Solve each inequality. |3c-6| ≥ 3First, to get rid of Absolute Value bars, Rewrite as two equations.

3c -6 ≥ 3 3c-6 ≤ -3

Now solve each equation and combine into one answer

Recipe to Solve Equations

Step1: Get x term(s) alone on one side of = sign.

Step2: Combine Like Terms.

Step3: Isolate x using opposite functions.

Step4: Plug x value back in to original question and check answer.

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CH4-5 Compound InequalitiesHow To Use It:3c -6 ≥ 3 3c-6 ≤ -3 +6 +6 +6 +63c ≥ 9 3c ≤ +33 3 3 3c ≥ 3 c ≤ +1c ≤ +1 orc ≥ 3

Recipe to Solve Equations

Step1: Get x term(s) alone on one side of = sign.

Step2: Combine Like Terms.

Step3: Isolate x using opposite functions.

Step4: Plug x value back in to original question and check answer.

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