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?

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?

Quizlet Admin · Accepted Answer

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 $	extbf{\color{#c34632}D.}$

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

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

$$
x+2=3x-4
$$

$$
x=3x-6
$$

$$
-2x=-6
$$

$$
x=3	o 	ext{choice C}\color{white}	ag{1}
$$

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?