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Lecture 33

# MTH 108 Lecture 33: 10.7 System of Inequalities Notes Premium

3 Pages
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Department
Mathematics
Course Code
MTH 108
Professor
Lun- Yi Tsai

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MTH 108 Precalculus Mathematics II 10.7 System of Inequalities Notes L. Sterling Abstract Provide a generalization to each of the key terms listed in this section. Solving Inequalities With Absolute Value Inequalities With Absolute Value Theorem If both a is any positive number and that x is an algebraic expression then the following will occur: jxj < a is equaled to ▯a < x < a jxj ▯ a is equaled to ▯a ▯ x ▯ a In Other Words : jxj < a is equaled to ▯a < x and x > a jxj ▯ a is equaled to ▯a ▯ x and x ▯ a Tip With Solving Inequalities Sign Interval Notation Formation < ( ) ▯ [ ] > ( ) ▯ [ ] Solving Inequalities Using Sign Charts Main Tips ▯ What are the general steps to solve any quadratic inequalities by using a sign chart? – Get zero on one side of the imbalance and after that discover the x-captures of the quadratic capacity on the opposite side. – Plot the given x-values of the various x-intercepts captures on a number line, which will help the number line into interims [aka Intervals]. – Decide a testing value from every interim and substitute it into the quadratic capacity to decide the sign, which is normally either positive or negative, of the capacity in that certain interim. – Analyze the disparity found in the initial step and ﬁgure out which interims from the previous step fulﬁll the imbalance. – On the oﬀ chance that the disparity, or inequality, is either ▯ or even ▯, make certain to incorporate the x-values of the possible x-intercepts as a feature of the arrangement. 1 Solving Inequalities With Absolute Value Inequalities With Absolute Value Theorem If both a is any positive number and that x is an algebraic expression then the following will occur: jxj > a is equaled tox < ▯a or x > a jxj ▯ a is equaled tox ▯ ▯a or x ▯ a Tip With Solving Inequalities Sign Interval Notation Formation < ( ) ▯ [ ]
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