Answered

What is the solution to the equation [tex]\sqrt{5x - 7} = \sqrt{3x + 5}[/tex]?

A. [tex]x = 1[/tex]
B. [tex]x = 6[/tex]
C. [tex]x = 12[/tex]
D. [tex]x = 24[/tex]



Answer :

To solve the equation \(\sqrt{5x - 7} = \sqrt{3x + 5}\), let's proceed with the following steps:

1. Square both sides of the equation to eliminate the square roots:
[tex]\[ (\sqrt{5x - 7})^2 = (\sqrt{3x + 5})^2 \][/tex]
This simplifies to:
[tex]\[ 5x - 7 = 3x + 5 \][/tex]

2. Isolate the variable \(x\):
- Subtract \(3x\) from both sides to get the \(x\) terms together:
[tex]\[ 5x - 3x - 7 = 3x - 3x + 5 \][/tex]
This simplifies to:
[tex]\[ 2x - 7 = 5 \][/tex]

- Add 7 to both sides to isolate the term with \(x\):
[tex]\[ 2x - 7 + 7 = 5 + 7 \][/tex]
This simplifies to:
[tex]\[ 2x = 12 \][/tex]

- Finally, divide both sides by 2 to solve for \(x\):
[tex]\[ \frac{2x}{2} = \frac{12}{2} \][/tex]
This simplifies to:
[tex]\[ x = 6 \][/tex]

Therefore, the solution to the equation \(\sqrt{5x - 7} = \sqrt{3x + 5}\) is:
[tex]\[ x = 6 \][/tex]

From the given options, we select:
[tex]\( x = 6 \)[/tex].