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1/3h-4(2/3h-3)=2/3h-6 Please show work!!!!

 Sep 22, 2016
 #1
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13h(23h3)=23h6

expand brackets

13h23h+3=23h6

multiply by 3h

12+3(3h)=26(3h)

take hs to one side (ie -3(3h))

12=26(3h)3(3h)

-2

122=6(3h)3(3h)

times out brackets

122=18h9h

combine

3=27h

×-1

3=27h

multiply by 127

327=27h27

simplify

h=327

common factors

h=3(1)3(9)

cancel out

h=19

ta dah!

 Sep 22, 2016
 #2
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Solve for h:
h/3-4 ((2 h)/(3)-3) = (2 h)/(3)-6

Put each term in (2 h)/(3)-3 over the common denominator 3: (2 h)/(3)-3 = (2 h)/3-(9)/3:
h/3-4(2 h)/3-(9)/3 = (2 h)/(3)-6

(2 h)/3-(9)/3 = (2 h-9)/3:
h/3-4(2 h-9)/3 = (2 h)/(3)-6

h/3-(4 (2 h-9))/3 = (h-4 (2 h-9))/3:
(h-4 (2 h-9))/3 = (2 h)/(3)-6

-4 (2 h-9) = 36-8 h:
(h+36-8 h)/3 = (2 h)/(3)-6

h-8 h = -7 h:
(-7 h+36)/3 = (2 h)/(3)-6

Put each term in (2 h)/(3)-6 over the common denominator 3: (2 h)/(3)-6 = (2 h)/3-(18)/3:
(36-7 h)/3 = (2 h)/3-(18)/3

(2 h)/3-(18)/3 = (2 h-18)/3:
(36-7 h)/3 = (2 h-18)/3

Multiply both sides by 3:
36-7 h = 2 h-18

Subtract 2 h from both sides:
36+(-7 h-2 h) = (2 h-2 h)-18

-7 h-2 h = -9 h:
-9 h+36 = (2 h-2 h)-18

2 h-2 h = 0:
36-9 h = -18

Subtract 36 from both sides:
(36-36)-9 h = -18-36

36-36 = 0:
-9 h = -18-36

-18-36 = -54:
-9 h = -54

Divide both sides of -9 h = -54 by -9:
(-9 h)/(-9) = (-54)/(-9)

(-9)/(-9) = 1:
h = (-54)/(-9)

The gcd of -54 and -9 is -9, so (-54)/(-9) = (-9×6)/(-9×1) = (-9)/(-9)×6 = 6:
Answer: |h = 6

 Sep 23, 2016

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