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We want to solve the following equation. 2^(x)=2+3x One of the solutions is x~~3.7. Find the other solution. Hint: Use a graphing calculator. Round your answer to the nearest tenth. x~~◻

We want to solve the following equation.\newline2x=2+3x2^{x}=2+3 x\newlineOne of the solutions is x≈3.7 x \approx 3.7 .\newlineFind the other solution.\newlineHint: Use a graphing calculator.\newlineRound your answer to the nearest tenth.\newlinex≈□x \approx \square

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Q. We want to solve the following equation.\newline2x=2+3x2^{x}=2+3 x\newlineOne of the solutions is x≈3.7 x \approx 3.7 .\newlineFind the other solution.\newlineHint: Use a graphing calculator.\newlineRound your answer to the nearest tenth.\newlinex≈□x \approx \square
  1. Understand Problem: Understand the problem and the given information.\newlineWe are given the equation 2x=2+3x2^{x} = 2 + 3x and we know that one solution is approximately x=3.7x = 3.7. We need to find the other solution using a graphing calculator, as suggested by the hint. We will graph both sides of the equation and look for the point(s) of intersection.
  2. Graph Equations: Graph the function y=2xy = 2^{x} and the line y=2+3xy = 2 + 3x using a graphing calculator.\newlineBy graphing these two equations, we can visually inspect where they intersect. We already know one intersection point is around x=3.7x = 3.7, so we are looking for any other points where the graphs cross.
  3. Identify Intersection Points: Identify the intersection point(s) other than x=3.7x = 3.7. Using the graphing calculator, we can use the ＂Intersect＂ feature to find the exact point of intersection. Since we are looking for the solution other than x=3.7x = 3.7, we focus on the part of the graph where x<3.7x < 3.7.
  4. Find Other Solution: Find the other solution and round it to the nearest tenth.\newlineAfter using the graphing calculator, we find that the other intersection point is approximately x=−0.2x = -0.2. This is the other solution to the equation 2x=2+3x2^{x} = 2 + 3x.

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