Solve the equation [tex]$\sqrt[1]{5 x}-4=1$[/tex]
A) [tex]$x=125$[/tex]
B) [tex]$x=625$[/tex]
C) [tex]$x=81 / 5$[/tex]
D) [tex]$x=25$[/tex]
Answer (2)
Add 4 to both sides of the equation: 1 5 x = 5 .
Simplify the equation: 5 x = 5 .
Divide both sides by 5: x = 1 .
Assuming the equation was intended to be 3 5 x − 4 = 1 , the solution is x = 25 .
Explanation
Understanding the Problem We are given the equation 1 5 x − 4 = 1 and asked to solve for x . This means we need to isolate x on one side of the equation.
Isolating the Term with x First, we add 4 to both sides of the equation to isolate the term with x : 1 5 x − 4 + 4 = 1 + 4 1 5 x = 5
Simplifying the Equation Since 1 5 x is simply 5 x , the equation becomes: 5 x = 5
Solving for x Now, we divide both sides of the equation by 5 to solve for x : 5 5 x = 5 5 x = 1
Re-examining the problem statement Therefore, the solution to the equation 1 5 x − 4 = 1 is x = 1 . However, this is not one of the answer choices. Let's re-examine the problem statement. It seems there might be a typo and the equation is actually 5 x − 4 = 1 . If that is the case, we proceed as follows:
Add 4 to both sides: 5 x = 5 Square both sides: 5 x = 25 Divide by 5: x = 5
Still not an answer choice. Let's assume the equation is 3 5 x − 4 = 1 . Then:
Add 4 to both sides: 3 5 x = 5 Cube both sides: 5 x = 125 Divide by 5: x = 25
This corresponds to answer choice D.
Final Answer Assuming the equation was intended to be 3 5 x − 4 = 1 , the solution is x = 25 .
Examples
When determining the side length of a cube with a specific volume, you might encounter cube roots. For instance, if you know the volume of a cube is 125 cubic units, finding the side length involves solving the equation s 3 = 125 , where s is the side length. This is similar to solving the equation 3 5 x = 5 , where you need to isolate x by cubing both sides. Understanding cube roots is essential in various fields, including engineering, architecture, and physics, where calculating volumes and dimensions is a common task.
The solution to the equation 1 5 x − 4 = 1 gives us x = 1 ; however, if we interpret it instead as 3 5 x − 4 = 1 , we find the solution is x = 25 , which corresponds to answer choice D.
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