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HiSET: Math : Rational and radical equations

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Example Question #1 : Rational And Radical Equations

Solve the following equation:

$\sqrt[3]{5-2x}+5=4$

Possible Answers:

x=-1

$x=\sqrt[3]{5}$

x=3

x=-2

x=2

Correct answer:

x=3

Explanation:

$\sqrt[3]{5-2x}+5=4$

The first step to solving an equation where is in a radical is to isolate the radical. To do this, we need to subtract the 5 from both sides.

$\sqrt[3]{5-2x}+5-5=4-5$

$\sqrt[3]{5-2x}=-1$

Now that the radical is isolated, clear the radical by raising both sides to the power of 3. Note:

$(-1)^3 = -1 \cdot -1 \cdot -1 = -1$

$(\sqrt[3]{5-2x})^3=(-1)^3$

{5-2x}=-1

Now we want to isolate the term. First, subtract the 5 from both sides.

{5-2x}-5=-1-5

-2x=-6

Finally, divide both sides by to solve for .

$\frac{-2x}{-2}=\frac{-6}{-2}$

x=3

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HiSET: Math : Rational and radical equations

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