Question

Solve the equation for x in terms of c

2/3(cx+1/2)-1/4=5/2.

A.x= 29/18c

B. x=9/4c

C.x=29/8c

D.x=27/8c

Answer 1

$solve\:for\:x,\:\frac{2}{3}\left(cx+\frac{1}{2}\right)-\frac{1}{4}=\frac{5}{2}$

$\mathrm{Add\:}\frac{1}{4}\mathrm{\:to\:both\:sides}$

$\frac{2}{3}\left(cx+\frac{1}{2}\right)-\frac{1}{4}+\frac{1}{4}=\frac{5}{2}+\frac{1}{4}$

$\frac{2}{3}\left(cx+\frac{1}{2}\right)=\frac{11}{4}$

$\mathrm{Multiply\:both\:sides\:by\:}3$

$3\cdot \frac{2}{3}\left(cx+\frac{1}{2}\right)=\frac{11\cdot \:3}{4}$

$2cx+1=\frac{33}{4}$

$\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}$

$2cx+1-1=\frac{33}{4}-1$

$2cx=\frac{29}{4}$

$\mathrm{Divide\:both\:sides\:by\:}2c$

$x=\frac{29}{8c}$

Therefore, correct option is C. option.

C. x=29/8c