Type the correct answer in the box. Round your answer to the nearest hundredth. Find the solution to the equation using a table of values. [tex]|2 x-1|=\sqrt{x}+3[/tex] The solution to the equation is [tex]x=[/tex] $\square$.
Answer (2)
We are given the equation ∣2 x − 1∣ = x + 3 .
We need to find the solution to this equation using a table of values.
By testing values of x and refining the search, we find the approximate solution.
The solution to the equation, rounded to the nearest hundredth, is 2.84 .
Explanation
Understanding the Problem We are given the equation ∣2 x − 1∣ = x + 3 and asked to find the solution using a table of values, rounded to the nearest hundredth.
Setting up the Solution We can solve this equation by creating a table of values for x , ∣2 x − 1∣ , and x + 3 . We want to find the value of x for which ∣2 x − 1∣ is approximately equal to x + 3 .
Finding the Approximate Solution Let's start by testing some values of x . We can use small increments to find the approximate solution. After testing several values, we find that when x is around 2.84, the two sides of the equation are close to each other. We can use a calculator or a script to find a more precise value.
Refining the Solution Using a Python script, we can iterate through values of x with increments of 0.01 and check when the absolute difference between ∣2 x − 1∣ and x + 3 is less than 0.01. The script gives us the solution x = 2.84 .
Final Answer Therefore, the solution to the equation ∣2 x − 1∣ = x + 3 , rounded to the nearest hundredth, is x = 2.84 .
Examples
Imagine you are designing a bridge and need to calculate the stress on a certain point. The equation ∣2 x − 1∣ = x + 3 is a simplified version of the kind of equations engineers use to model physical systems. Finding the solution to this equation helps you determine the value of a variable that satisfies the given condition, which could be related to the stability or safety of the bridge. Solving such equations is crucial in engineering to ensure structures are safe and efficient.
To find the solution to the equation ∣2 x − 1∣ = x + 3 , we create a table of values for x , calculate both sides, and find that the approximate solution is x = 2.84 .
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