Question

-2|5x-1|-3=11 and -2|5x-1|-3=-11

Answer 1

Answer : The values of x are $\frac{-3}{5}$ and 1.

Step-by-step explanation :

The given equation is:

$-2|5x-1|-3=-11$

The term -3 is moved or added to the right hand side.

$-2|5x-1|=-11+3$

$-2|5x-1|=-8$

The term -2 is divided to the right hand side.

$|5x-1|=\frac{-8}{-2}$

$|5x-1|=4$

Clear the absolute-value bars by splitting the equation into two cases. One for the positive case and the other for the negative case.

Negative case : $-(5x-1)=4$

Positive case : $(5x-1)=4$

Now solve both the cases.

Negative case : $-(5x-1)=4$

$-5x+1=4$

$-5x=4-1$

$-5x=3$

$x=\frac{-3}{5}$

and,

Positive case : $(5x-1)=4$

$5x=4+1$

$5x=5$

$x=1$

Therefore, the values of x are $\frac{-3}{5}$ and 1.