Solve the equation [tex]\sqrt{2 x}-1=3[/tex]
A) [tex]x=16[/tex]
B) [tex]x=4[/tex]
C) [tex]x=8[/tex]
D) [tex]x=2[/tex]
Answer (1)
Add 1 to both sides of the equation: 2 x = 4 .
Square both sides: 2 x = 16 .
Divide by 2: x = 8 .
The solution is 8 .
Explanation
Understanding the Problem We are given the equation 2 x − 1 = 3 and asked to solve for x . Our goal is to isolate x on one side of the equation.
Isolating the Square Root First, we add 1 to both sides of the equation to isolate the square root term: 2 x − 1 + 1 = 3 + 1 2 x = 4
Eliminating the Square Root Next, we square both sides of the equation to eliminate the square root: ( 2 x ) 2 = 4 2 2 x = 16
Solving for x Finally, we divide both sides of the equation by 2 to solve for x : 2 2 x = 2 16 x = 8
Final Answer Therefore, the solution to the equation 2 x − 1 = 3 is x = 8 . Looking at the multiple-choice options, we see that option C) x = 8 is the correct answer.
Examples
Imagine you are designing a square garden and need to determine the length of the sides. If the diagonal of the garden can be represented by the equation 2 x − 1 = 3 , where x relates to the area, solving for x helps you find the exact dimensions needed for your design. This application demonstrates how solving equations involving square roots can be directly applied in practical scenarios like garden design or any situation involving geometric measurements.
