Answer:
The solution is [tex]x = -1[/tex]
Step-by-step explanation:
We have the following equation:
[tex]\sqrt[3]{5x-3} + 8 = 6[/tex]
We place everything with the root on one side, everything without on the other site of the equality. So:
[tex]\sqrt[3]{5x-3} = -2[/tex]
Elevating both sides to 3, we can isolate x
[tex]\sqrt[3]{5x-3}^{3} = (-2)^{3}[/tex]
[tex]5x-3 = -8[/tex]
[tex]5x = -5[/tex]
[tex]x = -1[/tex]
Checking
[tex]\sqrt[3]{5(-1) - 3)} + 8 = \sqrt[3]{-8} + 8 = -2 + 8 = 6[/tex]
