BIM Alg I: Ch 2.3 Solving inequalities using Mult/Div

BIM Alg I: Ch 2.3 Solving inequalities using Mult/Div

Order of Numbers

2   $<$  4     

Also

2 * (2)  $<$  2 * (4)

4  $<$  8 

Order of Numbers Division

   4   $>$  2

4/2  $>$  2/2
     2 $>$  1

Math Conclusion

 Multiplying or Dividing by Positive Numbers causes no change in inequality

What if I multiply by a NEGATIVE number?

2   $<$  5
Multiply by a -1?
-1 * (2)  $<$  -1 * (5)
-2  $>$  -5
Wow!  It switched the inequality!!!!!!

What if I divide by a NEGATIVE number?

2   $<$  5
2/-1  $<$  5/-1
-2  $>$  -5
Wow!!!  Dividing by negative number switched the inequality also.  What!!!!!

Applying to Inequalities Variable Expressions

No Big Deal
-2x   $\le$  8

-2x/-2  $\le$  8/-2
x  $\ge$  -4

Mathematicians call "hard" problems interesting.

So (-2/3)x  $\ge$  10
Don't sweat the fraction.  
Take it in parts.
First get rid of the divisor.
3*(-2/3)x   $\ge$  3 * 10
-2x  $\ge$  30   We didn't multiply by negative so inequality didn't change.
Now (-2/-2)x  $\ge$  30/-2   Whamo!! 
x  $\le$  -15  The inequality switched.

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 code 44129968 Practice Quiz

Table Team Practice

-3/5 x  $\le$  -15

HW 2.3 p71-72: 3-39 every third problem.

Solution

-3/5 x  ≤   -15
5(-3/5) x ≤ 5 * -15
-3x ≤ -75
(-3/-3)x ≤ (-75/-3)
x  $\ge$  25

                  *------------>
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               25