Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$checkingupthesolution \frac{ 1 }{ 3 } = \frac{ 2 }{ x } - \frac{ 1 }{ 6 }$$

Answer

$$k=-(3*(2/x-1/6))/(e^2*c^2*h^2*n^2*g*u^2*p*t^2*s*o^2*l)$$

Solution


Simplify  \(check\imath ngupthesolut\imath on\times \frac{1}{3}\)  to  \(\frac{check\imath ngupthesolut\imath on}{3}\).
\[\frac{check\imath ngupthesolut\imath on}{3}=\frac{2}{x}-\frac{1}{6}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{{c}^{2}{h}^{2}{e}^{2}k{\imath }^{2}{n}^{2}g{u}^{2}p{t}^{2}s{o}^{2}l}{3}=\frac{2}{x}-\frac{1}{6}\]
Use Square Rule: \({i}^{2}=-1\).
\[\frac{{c}^{2}{h}^{2}{e}^{2}k\times -1\times {n}^{2}g{u}^{2}p{t}^{2}s{o}^{2}l}{3}=\frac{2}{x}-\frac{1}{6}\]
Simplify  \({c}^{2}{h}^{2}{e}^{2}k\times -1\times {n}^{2}g{u}^{2}p{t}^{2}s{o}^{2}l\)  to  \({c}^{2}{h}^{2}{e}^{2}k\times -{n}^{2}g{u}^{2}p{t}^{2}s{o}^{2}l\).
\[\frac{{c}^{2}{h}^{2}{e}^{2}k\times -{n}^{2}g{u}^{2}p{t}^{2}s{o}^{2}l}{3}=\frac{2}{x}-\frac{1}{6}\]
Regroup terms.
\[\frac{-{e}^{2}{c}^{2}{h}^{2}k{n}^{2}g{u}^{2}p{t}^{2}s{o}^{2}l}{3}=\frac{2}{x}-\frac{1}{6}\]
Move the negative sign to the left.
\[-\frac{{e}^{2}{c}^{2}{h}^{2}k{n}^{2}g{u}^{2}p{t}^{2}s{o}^{2}l}{3}=\frac{2}{x}-\frac{1}{6}\]
Multiply both sides by \(3\).
\[-{e}^{2}{c}^{2}{h}^{2}k{n}^{2}g{u}^{2}p{t}^{2}s{o}^{2}l=(\frac{2}{x}-\frac{1}{6})\times 3\]
Regroup terms.
\[-{e}^{2}{c}^{2}{h}^{2}k{n}^{2}g{u}^{2}p{t}^{2}s{o}^{2}l=3(\frac{2}{x}-\frac{1}{6})\]
Divide both sides by \(-{e}^{2}\).
\[{c}^{2}{h}^{2}k{n}^{2}g{u}^{2}p{t}^{2}s{o}^{2}l=-\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}}\]
Divide both sides by \({c}^{2}\).
\[{h}^{2}k{n}^{2}g{u}^{2}p{t}^{2}s{o}^{2}l=-\frac{\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}}}{{c}^{2}}\]
Simplify  \(\frac{\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}}}{{c}^{2}}\)  to  \(\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}}\).
\[{h}^{2}k{n}^{2}g{u}^{2}p{t}^{2}s{o}^{2}l=-\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}}\]
Divide both sides by \({h}^{2}\).
\[k{n}^{2}g{u}^{2}p{t}^{2}s{o}^{2}l=-\frac{\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}}}{{h}^{2}}\]
Simplify  \(\frac{\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}}}{{h}^{2}}\)  to  \(\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}}\).
\[k{n}^{2}g{u}^{2}p{t}^{2}s{o}^{2}l=-\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}}\]
Divide both sides by \({n}^{2}\).
\[kg{u}^{2}p{t}^{2}s{o}^{2}l=-\frac{\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}}}{{n}^{2}}\]
Simplify  \(\frac{\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}}}{{n}^{2}}\)  to  \(\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}}\).
\[kg{u}^{2}p{t}^{2}s{o}^{2}l=-\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}}\]
Divide both sides by \(g\).
\[k{u}^{2}p{t}^{2}s{o}^{2}l=-\frac{\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}}}{g}\]
Simplify  \(\frac{\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}}}{g}\)  to  \(\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}g}\).
\[k{u}^{2}p{t}^{2}s{o}^{2}l=-\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}g}\]
Divide both sides by \({u}^{2}\).
\[kp{t}^{2}s{o}^{2}l=-\frac{\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}g}}{{u}^{2}}\]
Simplify  \(\frac{\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}g}}{{u}^{2}}\)  to  \(\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}g{u}^{2}}\).
\[kp{t}^{2}s{o}^{2}l=-\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}g{u}^{2}}\]
Divide both sides by \(p\).
\[k{t}^{2}s{o}^{2}l=-\frac{\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}g{u}^{2}}}{p}\]
Simplify  \(\frac{\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}g{u}^{2}}}{p}\)  to  \(\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}g{u}^{2}p}\).
\[k{t}^{2}s{o}^{2}l=-\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}g{u}^{2}p}\]
Divide both sides by \({t}^{2}\).
\[ks{o}^{2}l=-\frac{\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}g{u}^{2}p}}{{t}^{2}}\]
Simplify  \(\frac{\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}g{u}^{2}p}}{{t}^{2}}\)  to  \(\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}g{u}^{2}p{t}^{2}}\).
\[ks{o}^{2}l=-\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}g{u}^{2}p{t}^{2}}\]
Divide both sides by \(s\).
\[k{o}^{2}l=-\frac{\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}g{u}^{2}p{t}^{2}}}{s}\]
Simplify  \(\frac{\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}g{u}^{2}p{t}^{2}}}{s}\)  to  \(\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}g{u}^{2}p{t}^{2}s}\).
\[k{o}^{2}l=-\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}g{u}^{2}p{t}^{2}s}\]
Divide both sides by \({o}^{2}\).
\[kl=-\frac{\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}g{u}^{2}p{t}^{2}s}}{{o}^{2}}\]
Simplify  \(\frac{\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}g{u}^{2}p{t}^{2}s}}{{o}^{2}}\)  to  \(\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}g{u}^{2}p{t}^{2}s{o}^{2}}\).
\[kl=-\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}g{u}^{2}p{t}^{2}s{o}^{2}}\]
Divide both sides by \(l\).
\[k=-\frac{\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}g{u}^{2}p{t}^{2}s{o}^{2}}}{l}\]
Simplify  \(\frac{\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}g{u}^{2}p{t}^{2}s{o}^{2}}}{l}\)  to  \(\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}g{u}^{2}p{t}^{2}s{o}^{2}l}\).
\[k=-\frac{3(\frac{2}{x}-\frac{1}{6})}{{e}^{2}{c}^{2}{h}^{2}{n}^{2}g{u}^{2}p{t}^{2}s{o}^{2}l}\]
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