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How do you solve $-(x-5)^(1/4)+7/3=2$ ?

1 Answer

May 24, 2017

$x = 406/81$

Explanation:

Subtract $7/3$ from both sides.

$-(x-5)^(1/4)+7/3-color(red)(7/3)=2-color(red)(7/3)$

$color(white)"XXXXX-."-(x-5)^(1/4) = -1/3$

Now multiply both sides by $-1$ .

$color(blue)(-1)(-(x-5)^(1/4))=color(blue)(-1)(-1/3)$

$color(white)"XXXXX"(x-5)^(1/4) = 1/3$

Next, take both sides to the power of $4$ .

$color(orange)((color(black)((x-5))^color(black)(1/4)))^color(orange)4 = color(orange)((color(black)(1/3)))^color(orange)4$

$(x-5) = 1/81$

Finally, add $5$ to both sides.

$x-5+color(limegreen)5=1/81+color(limegreen)5$

$x = 406/81$

Final Answer

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