Question

1. solve and write the solution using set notation if possible

14 + 3|2x - 5| = 7

Explanation:

Step1: Isolate the absolute value term

Subtract 14 from both sides of the equation \(14 + 3|2x - 5| = 7\):
\(3|2x - 5| = 7 - 14\)
\(3|2x - 5| = -7\)

Step2: Divide by 3

Divide both sides by 3:
\(|2x - 5| = \frac{-7}{3}\)

Step3: Analyze the absolute value

The absolute value of a number is always non - negative (i.e., \(|a|\geq0\) for any real number \(a\)). Here, we have \(|2x - 5|=\frac{-7}{3}\), but \(\frac{-7}{3}<0\). Since the absolute value of a number cannot be negative, there is no real solution to this equation.

Answer:

The solution set is \(\varnothing\) (the empty set)