Question 697747
I believe the exponent is {{{(5/3)}}}, so I would write it as
-5126= -6 -5(3x+22)^(5/3) or {{{-5126= -6 -5(3x+22)^(5/3)}}}
Since I cannot get those fractional exponents properly rendered, I'll try writing it as
{{{-5126= -6 -5(3x+22)}}}^(5/3)
We add 6 to both sides to get
{{{-5120= -5(3x+22)}}}^(5/3)
We multiply both sides times {{{(-1)}}} because I do not like minus signs.
(It's an old grudge from when one minus sign michieviously turned into a plus sign as I transcribed apolynomial to the flip side on the second page of a very long multi-part problem in an 11th grade midterm).
Multiplying times {{{(-1)}}} we get
{{{5120= 5(3x+22)}}}^(5/3)
We divide both sides by 5 to get
{{{1024= (3x+22)}}}^(5/3)
You know that {{{1024=2^10}}} , right?
Using that, we re-write the equation as
{{{2^10= (3x+22)}}}^(5/3)
We cube both sides of the equal sign to get
{{{(2^10)^3= ((3x+22)^(5/3))^3}}} --> {{{2^30=(3x+22)^5}}} --> {{{(2^6)^5=(3x+22)^5}}} --> {{{2^6=3x+22}}} --> {{{64=3x+22}}}
The rest is easy.
{{{64=3x+22}}} --> {{{64-22=3x}}} --> {{{42=3x}}} --> {{{42/3=3x/3}}} --> {{{highlight(x=14)}}}