Hello there!
We are given the equation:
[tex] \displaystyle \large{ |4x - 1| = 1}[/tex]
Definition/Property
[tex] \displaystyle \large{ |a| = \sqrt{ {a}^{2} } } \\ \displaystyle \large{ |a| = b \longrightarrow a = \pm b} \\ \displaystyle \large{ |a| = \begin{cases} a \: \: (x \geqslant 0) \\ - a \: \: (a < 0) \end{cases}}[/tex]
First, cancel the absolute value sign and write plus-minus beside 1.
[tex] \displaystyle \large{ |4x - 1| = 1} \\ \displaystyle \large{ 4x - 1 = \pm 1} \\ [/tex]
Break in two cases.
[tex] \displaystyle \large{ 4x - 1 = \begin{cases} 1 \\ - 1 \end{cases}} \\ \displaystyle \large{ 4x = \begin{cases} 1 + 1 \\ - 1 + 1 \end{cases}} \\ \displaystyle \large{ 4x = \begin{cases} 2 \\ 0 \end{cases}} \\ \displaystyle \large{ x = \begin{cases} \frac{2}{4} \\ \frac{0}{4} \end{cases}}[/tex]
Therefore, x = 0 or 1/2
Let me know if you have any questions!
Topic: Absolute Value Function - Equations
