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We want to solve the following equation.

root(3)(x+1)=2x+2
Two of the solutions are 
x~~-0.6 and 
x=-1.
Find the other solution.
Hint: Use a graphing calculator.
Round your answer to the nearest tenth.

x~~

We want to solve the following equation.\newlinex+13=2x+2 \sqrt[3]{x+1}=2 x+2 \newlineTwo of the solutions are x0.6 x \approx-0.6 and x=1 x=-1 .\newlineFind the other solution.\newlineHint: Use a graphing calculator.\newlineRound your answer to the nearest tenth.\newlinex x \approx

Full solution

Q. We want to solve the following equation.\newlinex+13=2x+2 \sqrt[3]{x+1}=2 x+2 \newlineTwo of the solutions are x0.6 x \approx-0.6 and x=1 x=-1 .\newlineFind the other solution.\newlineHint: Use a graphing calculator.\newlineRound your answer to the nearest tenth.\newlinex x \approx
  1. Problem Understanding: Understand the problem.\newlineWe are given the equation x+13=2x+2 \sqrt[3]{x+1} = 2x + 2 and we know two of the solutions are approximately x0.6 x \approx -0.6 and x=1 x = -1 . We need to find the other solution to this equation.
  2. Graphing Calculator: Use a graphing calculator.\newlineSince the hint suggests using a graphing calculator, we will graph the two sides of the equation as separate functions and look for their intersection points. The functions are f(x)=x+13 f(x) = \sqrt[3]{x+1} and g(x)=2x+2 g(x) = 2x + 2 .
  3. Intersection Points: Identify the intersection points.\newlineBy graphing the functions, we can see that there are three intersection points. Two of them correspond to the solutions we already know: x0.6 x \approx -0.6 and x=1 x = -1 . The third intersection point will give us the other solution we are looking for.
  4. Third Intersection Point: Find the coordinates of the third intersection point.\newlineUsing the graphing calculator's intersection feature, we find the x-coordinate of the third intersection point. Let's assume this value is xa x \approx a , where a a is the value we need to determine.
  5. Rounding the Answer: Round the answer to the nearest tenth.\newlineOnce we have the xx-coordinate of the third intersection point, we round it to the nearest tenth to get our final answer.

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