Question

Solve for x if sqrt (3x-8) + 1 = sqrt (x+5)

Answer 1

The solution of x in the given expression $\mathbf{\sqrt{(3x-8)}+1 = \sqrt{(x+5)}}$ is 4. However, if it is $\mathbf{\sqrt{(3x-8)+1} = \sqrt{(x+5)}}$, it is 6.

What is the solution to algebraic expression?

The solution to the given algebra expression involving surds can be seen in the steps below.

Given that:

$\mathbf{\sqrt{(3x-8)}+1 = \sqrt{(x+5)}}$

Remove the square roots, we have:

12x - 32 = 4x² - 48x + 144

Solving the quadratic equation at the RHS and equating it to LHS, we have:

x = 11, x = 4

Verifying the solutions by replacing the value of x with the given equation:

• x = 11 False
• x = 4 True

Therefore, we can conclude that the value of x = 4

NOTE:

Given that:

$\mathbf{\sqrt{(3x-8+1)} = \sqrt{(x+5)}}$

Square both sides

3x - 7 = x +5

Solve for x

3x - x = 5 + 7

2x = 12

x = 6

Learn more about solving to algebraic expressions here:

brainly.com/question/4344214

#SPJ1