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Elena is solving the following equation for x. root(3)(3x-5)+2=7 Her first few steps are given below. {:[root(3)(3x-5)=5],[(root(3)(3x-5))^(3)=(5)^(3)],[3x-5=125]:} Is it necessary for Elena to check her answers for extraneous solutions? Choose 1 answer: (A) Yes (B) No

Elena is solving the following equation for x x .\newline3x−53+2=7 \sqrt[3]{3 x-5}+2=7 \newlineHer first few steps are given below.\newline3x−53amp;=5(3x−53)3amp;=(5)33x−5amp;=125 \begin{aligned} \sqrt[3]{3 x-5} & =5 \\ (\sqrt[3]{3 x-5})^{3} & =(5)^{3} \\ 3 x-5 & =125 \end{aligned} \newlineIs it necessary for Elena to check her answers for extraneous solutions?\newlineChoose 11 answer:\newline(A) Yes\newline(B) No

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Q. Elena is solving the following equation for x x .\newline3x−53+2=7 \sqrt[3]{3 x-5}+2=7 \newlineHer first few steps are given below.\newline3x−53=5(3x−53)3=(5)33x−5=125 \begin{aligned} \sqrt[3]{3 x-5} & =5 \\ (\sqrt[3]{3 x-5})^{3} & =(5)^{3} \\ 3 x-5 & =125 \end{aligned} \newlineIs it necessary for Elena to check her answers for extraneous solutions?\newlineChoose 11 answer:\newline(A) Yes\newline(B) No
  1. Start with equation: Elena starts with the equation:\newline3x−53+2=7 \sqrt[3]{3x - 5} + 2 = 7 \newlineShe wants to isolate the cube root term, so she subtracts 22 from both sides of the equation:\newline3x−53=5 \sqrt[3]{3x - 5} = 5
  2. Subtract to isolate: Next, Elena raises both sides of the equation to the power of 33 to eliminate the cube root:\newline(3x−53)3=53 (\sqrt[3]{3x - 5})^3 = 5^3 \newlineThis gives us:\newline3x−5=125 3x - 5 = 125
  3. Raise to eliminate: Elena then adds 55 to both sides of the equation to solve for x:\newline3x=130 3x = 130
  4. Add to solve for x: Finally, Elena divides both sides by 33 to find the value of x:\newlinex=1303 x = \frac{130}{3}

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