Answer:
a) There is no solution to the equation.
b) Solution: x = 16
Explanation:
Hi there!
a) Let´s write the equation:
√(x + 5) - 9 = -12
add 9 to both sides of the equation
√(x + 5) = -12 + 9
√(x + 5) = -3
Square both sides of the equation
x + 5 = 9
Subtract 5 to both sides
x = 9 - 5
x = 4
Let´s check the solution:
√(x + 5) - 9 = -12
√(4 + 5) - 9 = -12
√9 - 9 = -12
3 - 9 = -12
-6 ≠ -12
Then x = 4 is not a solution to the equation.
b) Let´s write the equation:
√(4x - 7) = √(3x + 9)
square both sides of the equation
4x - 7 = 3x + 9
subtract 3x and add 7 to both sides of the equation
4x - 3x = 9 + 7
x = 16
Let´s check the solution:
√(4x - 7) = √(3x + 9)
x = 16
√(4(16) - 7) = √(3(16) + 9)
√57 = √57
Then x = 16 is the solution to the equation