D. The value of x in terms of c is [tex]x=\frac{29}{8c}[/tex]
What is the value of x ?
The given equation is [tex]\frac{2}{3}(cx+ \frac{1}{2})-\frac{1}{4}=\frac{5}{2}[/tex]
Solving we get,
First we have to add 1/4 in both sides,
[tex]\frac{2}{3}(cx+ \frac{1}{2})-\frac{1}{4}+\frac{1}{4}=\frac{5}{2}+\frac{1}{4}[/tex]
⇒ [tex]\frac{2}{3}(cx+ \frac{1}{2})=\frac{5}{2}+\frac{1}{4}[/tex]
⇒ [tex]\frac{2}{3}(cx+ \frac{1}{2})=\frac{10+1}{4}[/tex]
⇒ [tex]\frac{2}{3}(cx+ \frac{1}{2})=\frac{11}{4}[/tex]
⇒ [tex](cx+ \frac{1}{2})=\frac{11}{4}*\frac{3}{2}[/tex]
⇒ [tex](cx+\frac{1}{2} )=\frac{33}{8}[/tex]
⇒ [tex]cx = \frac{33}{8} -\frac{1}{2}[/tex]
⇒ [tex]cx = \frac{33-4}{8}[/tex]
⇒ [tex]cx=\frac{29}{8}[/tex]
⇒ [tex]x=\frac{29}{8c}[/tex]
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