Term
| What is the Addition Property of Inequalities when a is less than b? |
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Definition
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Term
| What is the Addition Property of Inequalities when a>b? |
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Definition
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Term
| What does the addition property state? |
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Definition
| The direction of an inequality remains unchanged if the same number is added to each side. |
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Term
| According to the Addition Property of Inequalities if x < 4, what? |
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Definition
| x < (-4) < 4 + (-4) or x-4 < 0 |
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Term
How do you solve a problem in this form?
if x < a, then x-a ____b? |
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Definition
The answer is always the inequality symbol the problem began with.
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In this case the answer is < |
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Term
| Infinity symbols when written in interval notation are always enclosed in what? |
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Definition
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Term
| In interval notation numbers that are included are enclosed in what? |
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Definition
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Term
| In interval notation numbers that are excluded are enclosed in what? |
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Definition
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Term
| Numbers that are less/greater than are enclosed in what when written in interval notation? |
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Definition
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Term
| Numbers that are less/greater than or equal to are enclosed in what when written in interval notation? |
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Definition
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Term
| The solution set for inequalities is written in what notation? |
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Definition
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Term
| In an inequality equation, whenever a negative number is multiplied or divided on both sides of the equation what happens to the inequality symbol? |
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Definition
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Term
| How do you make a/b equal a? |
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Definition
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Term
| How do you make b/a equal b? |
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Definition
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Term
| How do you solve a compound inequality? |
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Definition
1.)Complete each inequality equation
2.)Write each inequality in Interval Notation
3.)Write the two inequalities in interval notation as being an intersection if it is an "And" compound.
4.)Write the two inequalities in interval notation as being a union if it is an "Or" compound. |
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Term
| If A is less than or equal to B and C is negative, then what? |
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Definition
| A/C is Less than or Equal to B/C |
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Term
| If all the solutions of one inequality equation are in another when completing a compound inequality, then when writing them in interval notation there is no reason to be what? |
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Definition
| Redundant, this means that rather than using a symbol to connect two interval notations, they can simply be written as one that encompasses all of their shared solutions. |
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Term
How to solve a polynomial inequality in this form?
(x+a)(x+b)(x-b) greater than or equal to zero |
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Definition
1.)Set each statement to equal zero and solve for x.
x=-a
x=-b
x=b
2.)Plot -a and b on the number line, using brackets since the greater than or equal to symbol is used.
3.)Four intervals determine the three points -a,-b, and b. Those intervals are:
(-infinity,-a)(-a,-b)(-b,b)(b,infinity)
4.)Choose a test point (any real number) from each interval and plug it into the following in the place of x:
(x+a) (x+b) (x-b)
Then, mark which solutions are positive and negative by placing the appropriate symbol next to each one and then multiplying the positive and negative symbols together to come up with either a positive or negative result.
5.) If a test point has a negative result then its interval does not satisfy the inequality.
6.)If a test point's result is positive, then the interval does satisfy the inequality.
7.)Graph the intervals that satisfy the inequality on the number line, if they form one big line write their intervals as intersecting each other, if they do not then write them as being union with one another.
(Be sure to make everything included) |
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