Solve the following equation for [tex]$y$[/tex]: [tex]$2+\sqrt{4 y}-3=11$[/tex].
A. [tex]$y=3$[/tex]
B. [tex]$y=18$[/tex]
C. [tex]$y=6$[/tex]
D. [tex]$y=36$[/tex]
Answer (2)
Isolate the square root term: 4 y = 11 − 2 + 3 .
Simplify: 4 y = 12 .
Square both sides: 4 y = 144 .
Solve for y : y = 36 .
Explanation
Problem Analysis We are given the equation 2 + 4 y − 3 = 11 and asked to solve for y .
Isolating the Square Root First, we isolate the square root term by adding 3 and subtracting 2 from both sides of the equation: 4 y = 11 − 2 + 3
Simplifying Next, we simplify the right side of the equation: 4 y = 12
Squaring Both Sides Now, we square both sides of the equation to eliminate the square root: ( 4 y ) 2 = 1 2 2 4 y = 144
Solving for y Finally, we divide both sides by 4 to solve for y : y = 4 144 y = 36
Final Answer Therefore, the solution to the equation is y = 36 .
Examples
Imagine you are designing a square garden and need to determine the length of each side. If the area of the garden is related to a variable in an equation similar to the one we solved, finding the value of that variable helps you calculate the exact dimensions of your garden. For instance, if the area of the garden is 4 y and you know that 4 y = 12 , solving for y will give you the necessary information to plan your garden effectively. This type of problem-solving is useful in various real-world scenarios, from construction to landscape design.
By isolating the square root in the equation and squaring both sides, we find that y = 36 . Thus, the answer is option D. This process demonstrates how to solve for a variable when a square root is involved.
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