Absolute Value Equations #1

l5x+6l + 2= 6x - 3

Since absolute value is either a positive number or 0 and in this case, x cannot equal 0,

l5x+6l + 2 = 6x - 3 becomes 5x+6 + 2 = 6x - 3

And after solving this equation, we obtain x=11.

You must also consider that the value inside the absval could be a negative number.

So, -(5x + 6) = 6x - 5 ======>x = - 1/11 and substituting into initial equation shows that that solution is invalid. Only x = 11 works.

$|5x+6| + 2 = 6x - 3 \implies \begin{cases} \text{For }x < - \dfrac 65 & \implies - 5x - 6 + 2 = 6x - 3 & \implies x = - \dfrac 1{11} \not < - \dfrac 65 \color{#D61F06} \text{ rejected} \\ \text{For }x \ge - \dfrac 65 & \implies 5x + 6 + 2 = 6x - 3 & \implies x = \boxed{11} > - \dfrac 65 \color{#3D99F6} \text{ accepted} \end{cases}$

l5x+6l + 2 = 6x - 3 becomes 5x+6 + 2 = 6x - 3 after that used the addition property of equalities then it will become 6x-5x = 3+6+2 perform the equation x=11 then check it to the original equation ;)