Question

2.
a. $\frac{1}{4}(12 - 4x)=3 - x$
b. $x - 3 = 3 - x$
c. $x - 3 = 3 + x$

Explanation:

Step1: Expand left side (a)

$\frac{1}{4}(12 - 4x) = 3 - x$
$3 - x = 3 - x$

Step2: Simplify equation (a)

$-x + x = 3 - 3$
$0 = 0$

Step3: Isolate x terms (b)

$x - 3 = 3 - x$
$x + x = 3 + 3$

Step4: Solve for x (b)

$2x = 6$
$x = \frac{6}{2} = 3$

Step5: Isolate x terms (c)

$x - 3 = 3 + x$
$x - x = 3 + 3$

Step6: Simplify equation (c)

$0 = 6$

Answer:

a. All real numbers are solutions (identity)
b. $x = 3$
c. No solution (contradiction)