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Topic: **How to write absolute value****Question:**
How do I make an absolute value inequality for equal to or greater than -8 and less than or equal to 6

June 17, 2019 / By Kimberleigh

IIRC, one puts the two values in order that they would appear on the number line: -8 , 6 then we insert the absolute value expression (I'll use |x| for this example) -8 |x| 6 then we insert the less-than-or-equal-to symbol between the variable and the values: -8 ≤ |x| ≤ 6 The left part, -8 ≤ |x|, is equivalent to |x | ≥ -8 EDIT: I am assuming that you only need to write it, not solve it.

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IIRC, one puts the two values in order that they would appear on the number line: -8 , 6 then we insert the absolute value expression (I'll use |x| for this example) -8 |x| 6 then we insert the less-than-or-equal-to symbol between the variable and the values: -8 ≤ |x| ≤ 6 The left part, -8 ≤ |x|, is equivalent to |x | ≥ -8 EDIT: I am assuming that you only need to write it, not solve it.

|x+1| equal-to-or-less-than 7 |x+1| <= 7 - take the difference between -8 and +6, which is 14, then divide by 2 = 7 In order for x to land on -8 or +6 with 7 steps either add 7 to -8 = -1 or subtract 7 from +6 = -1. Insert in absolute inequality with x as above. The absolute inequality above gives the span of numbers between -8 and +6, both numbers included.

|x+1| equal-to-or-less-than 7 |x+1| <= 7 - take the difference between -8 and +6, which is 14, then divide by 2 = 7 In order for x to land on -8 or +6 with 7 steps either add 7 to -8 = -1 or subtract 7 from +6 = -1. Insert in absolute inequality with x as above. The absolute inequality above gives the span of numbers between -8 and +6, both numbers included.

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Write it so -8 < = |x| < = 6... to solve it just use the properties... if |x|< a then x < a and x>-a If |x| > a then x> a or x < -a Then here there are two inequalitis and we need to find the intersection... a) |x|< =6 ==> -6 <= x < = 6 b) |x| > = -8 ==> x > = -8 or x < = 8 ... here is all real number. Then the solution is the intersection that is -6 <=x< = 6 OK!

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Let x = number of adults The amount of cash for tickets sold to adults = 8x Let y = number of students The amount of cash for tickets sold to students = 5y x + y <= 525 8x + 5y > 3000 You could solve this by graphing them - if using a graphing calculator, solve each for y then shade as appropriate. To solve it manually, do as you would if there were equalities instead of inequalities. The answers you would find would be the absolute minimum (round up to the nearest whole number, as you can't have half a person).

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