Question

8c+6j=5 for c

Answer 1

to solve for c...
1st add -6j on both side ==> 8c + 6j + (-6j) = 5 + (-6j)
Result: +6j and -6j will cancel on the left hand side... as you see it, you just transfer 6j on the other side but inverted sign (this is what we call TRANSPOSITION) ==> 8c = 5 - 6j
2nd multiple both side of the equation by 1/8 ==> (1/8)8c = (5 - 6j)(1/8) or in LaTex\[\left(\frac{1}{8}\right)8c=(5-6j)\left(\frac{1}{8}\right)\]\[\left(\frac{1}{\bcancel{8}}\right)\bcancel{8}c=\frac{5-6j}{8}\]\[c=\frac{5-6j}{8}\]the last step is intentional, we want to solve for c, but it is 8c, so we have to remove 8 on the left hand side, multiplying by the reciprocal of 8 is simply dividing 8c by 8... so 8 will cancel and c remains, and take note... what you do on left hand side must be done also on right hand side... this step is also known as CROSS MULTIPLICATION... instead of multiplying both side by 1/8... we simply divide the right hand side by 8... hope the procedure is clear... \(\ddot\smile\)