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Levart [38]
3 years ago
5

Who's is the solution set of the compound inequality 3.5x-10>-3 and 8x-9<39

Mathematics
2 answers:
katrin2010 [14]3 years ago
7 0
3.5x - 10 > - 3
3.5x > 7
x > 2

8x - 9 < 39
8x < 48
x < 6

x > 2 and x < 6
Hope it helped!!
velikii [3]3 years ago
4 0
3.5x-10>-3  add 10 to both sides

3.5x>7  divide both sides by 3.5

x>2

... now for the other inequality:

8x-9<39  add 9 to both sides

8x<48  divide both sides by 3

x<6

So we have x>2 and x<6, so the compound inequality is:

2<x<6  and this means that the solution set is:

x=(2, 6)
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Multiply both the numerator and denominator by 2+\sqrt3, which is called the "conjugate" of 2-\sqrt3:

\dfrac{5+\sqrt3}{2-\sqrt3}\cdot\dfrac{2+\sqrt3}{2+\sqrt3}

Why do we pick this number? Recall the difference of squares factorization:

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Now replace a=2 and b=\sqrt3. Then

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