Question

Solve for x Express your answer as an integers or in simplest radical form 1-x^3=9

Answer 1

`\large\boxed{\tt x = 2}`

Explanation:

`\textsf{We are asked to solve for x in the given equation.}`

`\textsf{We should know that x is cubed, meaning that it's multiplied by itself 3 times.}`

`\textsf{We should isolate x on the left side of the equation, then find x by cubic rooting}`

`\textsf{both sides of the equation.}`

`\large\underline{\textsf{How is this possible?}}`

`\textsf{To isolate variables, we use Properties of Equality to prove that expressions}`

`\textsf{are still equal once a constant has changed both sides of the equation. A Cubic}`

`\textsf{Root is exactly like a square root, but it's square rooting the term twice instead}`

`\textsf{of once.}`

`\large\underline{\textsf{For our problem;}}`

`\textsf{We should use the Subtraction Property of Equality to isolate x, then cubic root}`

`\textsf{both sides of the equation.}`

`\large\underline{\textsf{Solving;}}`

`\textsf{Subtract 1 from both sides of the equation keeping in mind the Subtraction}`

`\textsf{Property of Equality;}/tex]</p><p>[tex]\tt \\ot{1} - \\ot{1} - x^(3) = 9 - 1`

`\tt - x^(3) = 8`

`\textsf{Because x}^(3) \ \textsf{is negative, we should exponentiate both sides of the equation by}`

`\textsf{the reciprocal of 3, which is} \ \tt (1)/(3) .`

`\tt (- x^(3))^{(1)/(3)} = 8^{(1)/(3)}`

`\underline{\textsf{Evaluate;}}`

`\tt (- x^(3))^{(1)/(3)} \rightarrow -x^{3 * (1)/(3) } \rightarrow \boxed{\tt -x}`

`\textsf{*Note;}`

`\boxed{\tt A^{(1)/(C)} = \sqrt[\tt C]{\tt A}}`

`\tt 8^{(1)/(3)} \rightarrow \sqrt[3]{8} \rightarrow 2^(1) \rightarrow \boxed{\tt 2}`

`\underline{\textsf{We should have;}}`

`\tt -x=2`

`\textsf{Use the Division Property of Equality to divide each side of the equation by -1;}`

`\large\boxed{\tt x = 2}`