Question

What are the solutions to the equation 4|2x - 1| + 3 = 11 ?

Answer 1

Given the question in the question tab, the following are the solution steps to solve the equation

STEP 1: Write the given equation

`4\mleft|2x-1\mright|+3=11`

STEP 2: Solve for x

`\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} \\ (4|2x-1|)/(4)=(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=(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=-(1)/(2) \\ x=(3)/(2)\text{ or }-(1)/(2) \end{gathered}`

Hence, the values of x for the equation are:

`x=(3)/(2)\text{ or }-(1)/(2)`