Respuesta :
SOLUTION
Given the question in the question tab, the following are the solution steps to solve the equation
STEP 1: Write the given equation
[tex]4\mleft|2x-1\mright|+3=11[/tex]STEP 2: Solve for x
[tex]\begin{gathered} 4\mleft|2x-1\mright|+3=11 \\ \text{Subtract 3 from both sides} \\ 4\mleft|2x-1\mright|+3-3=11-3 \\ 4\mleft|2x-1\mright|=8 \\ \text{Divide both sides by 4} \\ \frac{4|2x-1|}{4}=\frac{8}{4} \\ |2x-1|=2 \\ \text{Apply absolute rul which states that:} \\ I\text{f }|u|=a,a>0\text{ then }u=a\text{ or }u=-a \\ \text{This implies that:} \\ 2x-1=2\text{ or }2x-1=-2 \\ 2x-1=2 \\ \text{Add 1 to both sides} \\ 2x-1+1=2+1 \\ 2x=3 \\ \text{Divide both sides by 2} \\ x=\frac{3}{2} \\ \\ 2x-1=-2 \\ \text{Add 1 to both sides} \\ 2x-1+1=-2+1 \\ 2x=-1 \\ \text{Divide both sides by 2} \\ x=-\frac{1}{2} \\ x=\frac{3}{2}\text{ or }-\frac{1}{2} \end{gathered}[/tex]Hence, the values of x for the equation are:
[tex]x=\frac{3}{2}\text{ or }-\frac{1}{2}[/tex]