Algebra 2 Part 8 Chapter 1

Service Description

The last notation Grandma did not have room for was with the same number line of 5 equal markings to the left of zero and 7 markings to the right of zero. We were recording various Interval Notations with specific Inequality Notations. The last one had an Inequality Notation of x < -2 v x >_5 with an Interval Notation of ( - eternity, -2) U [5, eternity). The line shows two separate thick lines going in opposite directions. One comes up from an open circle at two marks left of the zero turning left with an arrow; the other thick line comes up from a filled in circle or dot from the 5th mark right of the zero and turns right straight out with an arrow. Since this is all very hard Grandma is glad, we are moving to another section called Compound Linear Inequalities it goes on to say, "A 'compound inequality' in one variable consists of two inequalities connected by either "and" (^) or "or" (v). In general, each part may be solved separately and then the final answer written appropriately. Example 1.11 Solve 5x + 7 > 27 and 2x-8< 4 for x. Solution 5x +7 > 27 and 2x-8 < 4 5x > 20 2x < 12 x>4 and x< 6 4< x < 6 Example 1.12 Solve 3(x+1) <-6 or 5x - 14 > 21 for x Solution 3(x + 1) <_ -6 or 5x - 14 >_ 21 3x + 3 <_ -6 5x> 35 3x<_ -9 x >_7 x<_ -3 x<_ -3 or x >_7 "'Inequalities joined with "and" are often written together as in the next example. They are solved in the usual way. However, the same operation must be done to all 'three' parts of the 'inequality' to isolate the variable in the center. Example 1.13 Solve -5 <_4x -3 <_ 5 for x. Solution -5 <_ 4x - 3 <_ 5 +3 <_ + 3<_ +3 __________________ -2 /4 <_ 4x/4 <_8/4 -0.5 <_ x <_ 2 "Sometimes 'compound inequalities', especial ones involving "and"(^), may have no real solutions." Example 1.14 Solve 2x - 1< 3^6x -5> 19 for x. Solution 2x -1 <3 ^ 6x -5 > 19 2x < 4 6x > 24 x< 2 ^ x > 4 No numbers are both less than 2 and greater than 4. So the solution set for this problem is the 'empty set', which may be written as { } or no zero (but not as {no zero} ). Section Exercises Express each of the follow(finish in the next lesson)