Solve $\sqrt{5 x}+4=15$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution is $x=$ $\square$ .
(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.)
B. There is no solution.
Answer (2)
Subtract 4 from both sides: 5 x = 11 .
Square both sides: 5 x = 121 .
Divide by 5: x = 5 121 .
The solution is x = 5 121 .
Explanation
Problem Analysis We are given the equation 5 x + 4 = 15 and we want to solve for x . Our goal is to isolate x by performing algebraic operations on both sides of the equation.
Isolating the Square Root First, we subtract 4 from both sides of the equation to isolate the square root term: 5 x + 4 − 4 = 15 − 4 5 x = 11
Squaring Both Sides Next, we square both sides of the equation to eliminate the square root: ( 5 x ) 2 = 1 1 2 5 x = 121
Solving for x Now, we divide both sides by 5 to solve for x :
5 5 x = 5 121 x = 5 121
Checking for Extraneous Solutions We should check if this solution is extraneous by substituting x = 5 121 back into the original equation: 5 ( 5 121 ) + 4 = 15 121 + 4 = 15 11 + 4 = 15 15 = 15 Since the equation holds true, x = 5 121 is a valid solution.
Final Answer Therefore, the solution to the equation 5 x + 4 = 15 is x = 5 121 .
Examples
Imagine you are designing a square garden and need to determine the length of each side. If the area of the garden, represented by x , is related to the length of the fence required to enclose it by the equation 4 x + 2 = 10 , solving for x will tell you the area of the garden. This type of problem demonstrates how algebraic equations involving square roots can be used to solve practical problems related to geometry and design.
The solution to the equation 5 x + 4 = 15 is x = 5 121 .
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