winter, 2010-2011. ch4-1 inequalities and their graphs background: many times we don’t know the...
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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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