Absolute values

Absolute value is explained through this question:

Q # 1: Find the solution set of $|5x-3|-2=3$

Solution:

• First of all just write the equation,

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

• Simplify the equation

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

  $|5x-3|=5$

• Now we open the absolute value sign such as equate the value that is in the modulus sign one time with the positive of the other side and one time with the negative of other side,

  $5x-3=5$ or $5x-3=-5$

• Now both of these are simple linear equation and we will solve it as follows

  $5x=8$ or $5x=-2$

  $x=\frac{8}{5}$ or $x=\frac{-2}{5}$

• Now both of these answer are solutions

  Thus Solution set = $\{\frac{8}{5},\frac{-2}{5}\}$

Q # 2: Find the solution set of $|5x-3|-8=4$, where $x\in N$

Solution:

• First of all just write the equation,

  $|5x-3|-8=4$

• Simplify the equation

  $|5x-3|=8+4$

  $|5x-3|=12$

• Now we open the absolute value sign such as equate the value that is in the modulus sign one time with the positive of the other side and one time with the negative of other side,

  $5x-3=12$ or $5x-3=-12$

• Now both of these are simple linear equation and we will solve it as follows

  $5x=15$ or $5x=-9$

  $x=\frac{15}{5}$ or $x=\frac{-9}{5}$

  $x=3$ or $x=\frac{-9}{5}$

• Now here comes a trick. In the question they mentioned that $x\in N$ which means our solution set can only have natural numbers so we will be taking only 3 as our solution set and not $\frac{-9}{5}$ because it is not a natural number.

  Thus Solution set = $\{3\}$