Question

This one if to hard for me

Answer 1

x=0 , x = 1/2

Explanation:

(4x-1)=1 —> 4x-1=1—> 4x=1+1—> 4x=2 —> x=2/4 —> x= 1/2

-(4x-1)=1—>-4x+1=1—> 4x= 1-1 —> x=0

Answer 2

Hello there!

We are given the equation:

`\displaystyle \large`

Definition/Property

`\displaystyle \large{ |a| = \sqrt{ {a}^(2) } } \\ \displaystyle \largea \\ \displaystyle \large{ |a| = \begin{cases} a \: \: (x \geqslant 0) \\ - a \: \: (a < 0) \end{cases}}`

First, cancel the absolute value sign and write plus-minus beside 1.

`\displaystyle \large \\ \displaystyle \large{ 4x - 1 = \pm 1} \\`

Break in two cases.

`\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} (2)/(4) \\ (0)/(4) \end{cases}}`

Therefore, x = 0 or 1/2

Let me know if you have any questions!

Topic: Absolute Value Function - Equations