13h−(23h−3)=23h−6
expand brackets
13h−23h+3=23h−6
multiply by 3h
1−2+3(3h)=2−6(3h)
take hs to one side (ie -3(3h))
1−2=2−6(3h)−3(3h)
-2
1−2−2=−6(3h)−3(3h)
times out brackets
1−2−2=−18h−9h
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!
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