To solve the equation [tex]$\sqrt{5x - 3} = \sqrt{2x + 3}$[/tex], follow these steps:
1. Square both sides:
To eliminate the square roots, we square both sides of the equation:
[tex]\[
\left(\sqrt{5x - 3}\right)^2 = \left(\sqrt{2x + 3}\right)^2
\][/tex]
Simplifying the squares, we get:
[tex]\[
5x - 3 = 2x + 3
\][/tex]
2. Isolate the variable [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], we need to get all terms involving [tex]\(x\)[/tex] on one side and the constant terms on the other side. Begin by subtracting [tex]\(2x\)[/tex] from both sides:
[tex]\[
5x - 2x - 3 = 3
\][/tex]
Simplify the left side:
[tex]\[
3x - 3 = 3
\][/tex]
Next, add 3 to both sides to isolate the [tex]\(x\)[/tex] term:
[tex]\[
3x - 3 + 3 = 3 + 3
\][/tex]
Simplify:
[tex]\[
3x = 6
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
Divide both sides by 3:
[tex]\[
x = \frac{6}{3}
\][/tex]
Simplify the division:
[tex]\[
x = 2
\][/tex]
So, the solution to the equation [tex]\(\sqrt{5x - 3} = \sqrt{2x + 3}\)[/tex] is [tex]\(x = 2\)[/tex].
