If x=1+3a, find the value of a if 5/3(1+4a-x)-5/12=6a-3/4(2x-1)

Dear Student,

Please find below the solution to the asked query:

Given : x  =  1  + 3 a 

Then we find value of $\frac{5}{3\left(1 + 4 a - x\right)} -\frac{5}{12} = \frac{6 a -3}{4\left( 2 x - 1\right)}$  by substituting given value , As :

$$\begin{gathered} \frac{5}{3\left(1 + 4 \mathrm{a} -\left(1 + 3 \mathrm{a}\right) \right)} -\frac{5}{12} = \frac{6 \mathrm{a} -3}{4\left( 2 \left(1 + 3 \mathrm{a}\right) - 1\right)} \\ \Rightarrow \frac{5}{3\left(1 + 4 \mathrm{a} - 1 - 3 \mathrm{a} \right)} -\frac{5}{12} = \frac{6 \mathrm{a} -3}{4\left( 2 + 6 \mathrm{a} - 1\right)} \\ \Rightarrow \frac{5}{3 \mathrm{a}} -\frac{5}{12} = \frac{6 \mathrm{a} -3}{4\left( 6 \mathrm{a} + 1\right)} \\ \Rightarrow \frac{60 - 15 \mathrm{a}}{36 \mathrm{a}} = \frac{6 \mathrm{a} -3}{24 \mathrm{a} + 4} \\ \Rightarrow \left(60 - 15 \mathrm{a}\right)\left(24 \mathrm{a} + 4\right) = \left(36 \mathrm{a}\right)\left(6 \mathrm{a} -3\right) \\ \Rightarrow 1440 \mathrm{a} + 240 - 360 {\mathrm{a}}^2 - 60 \mathrm{a} = 216 {\mathrm{a}}^2 - 108 \mathrm{a} \\ \Rightarrow 576 {\mathrm{a}}^2 -1488 \mathrm{a} - 240 = 0 \\ \Rightarrow 16\left(36 {\mathrm{a}}^2 -93 \mathrm{a} - 15\right) = 0 \\ \mathbf{\Rightarrow }\mathbf{36}\mathbf{ }{\mathbf{a}}^{\mathbf{2}}\mathbf{ }\mathbf{-}\mathbf{93}\mathbf{ }\mathbf{a}\mathbf{ }\mathbf{-}\mathbf{ }\mathbf{15}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{0} \end{gathered}$$

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