Solve: [tex]\sqrt{7 f+5}=5[/tex]
Answer (2)
To solve the equation 7 f + 5 = 5 , we square both sides to eliminate the square root, then isolate f to find f = 7 20 .
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Square both sides: ( 7 f + 5 ) 2 = 5 2 which simplifies to 7 f + 5 = 25 .
Subtract 5 from both sides: 7 f = 20 .
Divide by 7: f = 7 20 .
The solution is 7 20 .
Explanation
Understanding the Problem We are given the equation 7 f + 5 = 5 . Our goal is to solve for f , which means we want to isolate f on one side of the equation.
Eliminating the Square Root To start, we square both sides of the equation to eliminate the square root: ( 7 f + 5 ) 2 = 5 2 This simplifies to: 7 f + 5 = 25
Isolating the Term with f Next, we subtract 5 from both sides of the equation to isolate the term with f : 7 f + 5 − 5 = 25 − 5 This simplifies to: 7 f = 20
Solving for f Finally, we divide both sides of the equation by 7 to solve for f : 7 7 f = 7 20 This gives us: f = 7 20
Final Answer Therefore, the solution to the equation 7 f + 5 = 5 is f = 7 20 .
Examples
Imagine you are designing a square garden and need to determine the length of each side. If the area of the garden is represented by the equation 4 x + 12 = 8 , where x is related to the side length, solving for x helps you find the exact dimensions needed. This type of algebraic problem is crucial in various fields like construction, landscaping, and even in optimizing space in urban planning.
