Answer:
The solution is -5 or 11
Step-by-step explanation:
We are given the equation;
[tex]4(3-x)^\frac{4}{3}-5=59[/tex]
We are supposed to solve the equation;
Taking 5 to the other side;
[tex]4(3-x)^\frac{4}{3}=59+5[/tex]
[tex]4(3-x)^\frac{4}{3}=64[/tex]
Dividing both sides by 4
[tex](3-x)^\frac{4}{3}=\frac{64}{4}[/tex]
[tex](3-x)^\frac{4}{3}=16[/tex]
We can cube both sides;
[tex]((3-x)^\frac{4}{3})^3=16^3[/tex]
[tex](3-x)^4=4096[/tex]
Then we can get the fourth root on both sides of the equation;
[tex]\sqrt[4]{ (3-x)^4} =\sqrt[4]{4096}[/tex]
We get;
[tex]3-x=+8 or -8[/tex]
Solving for x
[tex]3-x=8 and 3-x=-8[/tex]
Therefore;
[tex]x=-5 or 11[/tex]
Therefore, the solution is -5 or 11
