Question

solve:
$3 - |2x - 5| = 5$
a $left\\{\frac{2}{3}, \frac{2}{7}\
ight\\}$
b ${3, 7}$
c $left\\{\frac{3}{2}, \frac{7}{2}\
ight\\}$
d $\emptyset$

Explanation:

Step1: Isolate the absolute value

Subtract 3 from both sides:
$3 - |2x - 5| - 3 = 5 - 3$
$-|2x - 5| = 2$
Multiply both sides by -1:
$|2x - 5| = -2$

Step2: Analyze absolute value validity

The absolute value of any real number is non-negative, meaning $|a| \geq 0$ for all real $a$. Since $-2 < 0$, there is no real number $x$ that satisfies the equation.

Answer:

D. $\empty$ (empty set)