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???

Answer: they don't

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

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