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# Find the solution sets

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324
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19<5p+4<29

x+5>5 and x+4<3

(1/20)<(2-3x/20)<(2/5)

3x+5<8 or 9x>41

-25<5(x-5)<4

Jan 5, 2015

#1
+102390
+5

19<5p+4<29         subtract 4 from everything

15 < 5p < 25         divide everything by 5

3 <  p   <  5

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x+5>5 and x+4<3

x+5 >5    subtract  5 to both sides                  x+4<3   subtract 4 from both sides

x  > 0                                                           x < -1

"And"  means  "intersection"......in other words, where do these solutions overlap???

Thus, the solution is  { } ....  i.e., the empty set

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(1/20)<(2-3x/20)<(2/5)  ...first, multiply everything by 20 to clear the fractions

1 < 40 - 3x < 8       subtract 40 from both sides

-39 < -3x < -32      divide everything by -3 and remember to "reverse" the inequality signs

13 > x > 32/3

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3x+5<8 or 9x>41

3x+5<8   subtract 5 from both sides                     9x>41  divide both sides by 9

3x  < 3    divide both sides by 3                              x > 41/9

x  < 1

"Or"  means "union"

So, the union of these two answers is  (-∞, 1] U (41/9, ∞)

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-25<5(x-5)<4        divide everything by 5

-5 < x-5 < 4/5       add 5 to everything

0 < x < 29/5

-----------------------------------------------------------------------------------------------------------------------

Jan 5, 2015

#1
+102390
+5

19<5p+4<29         subtract 4 from everything

15 < 5p < 25         divide everything by 5

3 <  p   <  5

--------------------------------------------------------------------------------------------------------------------------

x+5>5 and x+4<3

x+5 >5    subtract  5 to both sides                  x+4<3   subtract 4 from both sides

x  > 0                                                           x < -1

"And"  means  "intersection"......in other words, where do these solutions overlap???

Thus, the solution is  { } ....  i.e., the empty set

--------------------------------------------------------------------------------------------------------------------------

(1/20)<(2-3x/20)<(2/5)  ...first, multiply everything by 20 to clear the fractions

1 < 40 - 3x < 8       subtract 40 from both sides

-39 < -3x < -32      divide everything by -3 and remember to "reverse" the inequality signs

13 > x > 32/3

--------------------------------------------------------------------------------------------------------------------------

3x+5<8 or 9x>41

3x+5<8   subtract 5 from both sides                     9x>41  divide both sides by 9

3x  < 3    divide both sides by 3                              x > 41/9

x  < 1

"Or"  means "union"

So, the union of these two answers is  (-∞, 1] U (41/9, ∞)

--------------------------------------------------------------------------------------------------------------------------

-25<5(x-5)<4        divide everything by 5

-5 < x-5 < 4/5       add 5 to everything

0 < x < 29/5

-----------------------------------------------------------------------------------------------------------------------

CPhill Jan 5, 2015