Question

In the equation below, for what value of c does x = 4?$\frac{1}{2}(2x+4)=3x-c$A -6 B -3 C 3 D 6 Jenn chose C as the correct answer. How did she get that answer?

Solution

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Since $x=4$, then we substitute it to the equation and solve for $c$:

$\dfrac{1}{2}(2(4)+4)=3(4)-c$

$\dfrac{1}{2}(8+4)=12-c$

$\dfrac{1}{2}(12)=12-c$

$6=12-c$

$-6=-c$

$6=c$

So, the correct answer is choice $\textbf{\color{#c34632}D.}$

Jenn must have substituted $c=4$ then solved for $x$ instead as shown:

$\dfrac{1}{2}(2x+4)=3x-4$

$x+2=3x-4$

$x=3x-6$

$-2x=-6$

$x=3\to \text{choice C}\color{white}\tag{1}$

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