Solve $$ \sqrt[3]{3 x-7}=-17 $$ Round your answer to the nearest tenth.

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UpStudy AI · Accepted Answer

Solve the equation $$ \sqrt[3]{3x-7}=-17 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\sqrt[3]{3x-7}=-17$$
- step1: Simplify the equation:
  $$\left(\sqrt[3]{3x-7}\right)^{3}=\left(-17\right)^{3}$$
- step2: Evaluate:
  $$3x-7=-4913$$
- step3: Move the constant to the right side:
  $$3x=-4913+7$$
- step4: Add the numbers:
  $$3x=-4906$$
- step5: Divide both sides:
  $$\frac{3x}{3}=\frac{-4906}{3}$$
- step6: Divide the numbers:
  $$x=-\frac{4906}{3}$$
- step7: Check the solution:
  $$x=-\frac{4906}{3}$$
The solution to the equation $$ \sqrt[3]{3x-7}=-17 $$ is $$ x=-\frac{4906}{3} $$ or $$ x=-1635.\dot{3} $$.

Rounding the answer to the nearest tenth, we have $$ x=-1635.3 $$.
$$ x = -1635.3 $$

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Round your answer to the nearest tenth.

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