Answer:
The equations are
(a) x/3 = 6
(b) (5x + 9)/2 = 12
(c) x/4 = 9/6
(d) 5/x = 20/8
The answers to the question are
(a) x = 18
(b) x = 3
(c) x = 6
(d) x = 2
Step-by-step explanation:
(a) x/3 = 6
Therefore x = 3×6 = 18
x =18
Substituting the value of x in the above equation, we have
18/6 = 3 verified
(b) (5x + 9)/2 = 12
Multiplying both sides by 2 gives
(5x + 9)/2 × 2 = 12×2 = 24
5x + 9 = 24 or x = (24-9)/5 = 3
Substituting the value of x in the above equation, we have
(5×3 + 9)/2 = 24/2 = 12 verified
x = 3
(c) x/4 = 9/6
Multiplying both sides by 4, we have
x/4×4 = 9/6×4 = 6
x = 6
Substituting the value of x in the above equation, we have
(6/4 = 9/6 = 3/2 verified
(d) 5/x = 20/8
Inverting both equations, we have
x/5 = 8/20
Multiplying both sides by 20 we have x/5 × 20 = 8/20 × 20 or 4x = 8 and x = 2
Substituting the value of x in the original equation, we have
2/5 = 2/5 = 8/20 verified
x = 2
![\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\ \quad \\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~{{ 4}} &,&{{ -1}}~) % (c,d) &&(~{{ -5}} &,&{{ -2}}~) \end{array}~~ % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ d=\sqrt{[-5-4]^2+[-2-(-1)]^2}\implies d=\sqrt{(-5-4)^2+(-2+1)^2} \\\\\\ d=\sqrt{(-9)^2+(-1)^2}\implies d=\sqrt{81+1}\implies d=\sqrt{82}](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%5C%5C%20%5Cquad%20%5C%5C%0A%5Cbegin%7Barray%7D%7Bccccccccc%7D%0A%26%26x_1%26%26y_1%26%26x_2%26%26y_2%5C%5C%0A%25%20%20%28a%2Cb%29%0A%26%26%28~%7B%7B%204%7D%7D%20%26%2C%26%7B%7B%20-1%7D%7D~%29%20%0A%25%20%20%28c%2Cd%29%0A%26%26%28~%7B%7B%20-5%7D%7D%20%26%2C%26%7B%7B%20-2%7D%7D~%29%0A%5Cend%7Barray%7D~~%0A%25%20%20distance%20value%0Ad%20%3D%20%5Csqrt%7B%28%7B%7B%20x_2%7D%7D-%7B%7B%20x_1%7D%7D%29%5E2%20%2B%20%28%7B%7B%20y_2%7D%7D-%7B%7B%20y_1%7D%7D%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0Ad%3D%5Csqrt%7B%5B-5-4%5D%5E2%2B%5B-2-%28-1%29%5D%5E2%7D%5Cimplies%20d%3D%5Csqrt%7B%28-5-4%29%5E2%2B%28-2%2B1%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0Ad%3D%5Csqrt%7B%28-9%29%5E2%2B%28-1%29%5E2%7D%5Cimplies%20d%3D%5Csqrt%7B81%2B1%7D%5Cimplies%20d%3D%5Csqrt%7B82%7D)
