Question

The table below shows two equations:
Equation 1 |4x - 3|- 5 = 4
Equation 2 |2x + 3| + 8 = 3

Which statement is true about the solution to the two equations? (4 points)

Equation 1 and equation 2 have no solutions.
Equation 1 has no solution and equation 2 has solutions x = -4, 1.
The solutions to equation 1 are x = 3, -1.5 and equation 2 has no solution.
The solutions to equation 1 are x = 3, -1.5 and equation 2 has solutions x = -4, 1.

Answer 1

\(\large {|4x - 3|- 5 = 4\implies |4x - 3|=4+5\implies|4x - 3|=9\\ \quad \\

|4x - 3|=9\implies
\begin{cases}
+(4x - 3)=9\\ \quad \\
-(4x - 3)=9
\end{cases}\\ \quad ------------------------\\
|2x + 3| + 8 = 3\implies|2x + 3| = 3-8\implies|2x + 3| =-5\\ \quad \\
|2x + 3| =-5\implies
\begin{cases}
+(2x + 3) =-5\\ \quad \\
-(2x + 3) =-5
\end{cases}}\)