Question

Match the operation with its inverse operation you would use to solve an equation for a variable.(7 points)Multiplication, x^3, √x, Subtraction, Addition, Division, x^2
Multiplication
Subtraction
Addition
Division
x^2
x^3
√x
3√x

Answer 1

The equation: x^3=−8 will have how many solutions for x ?(1 point)
One solution: x = -8/3 since the inverse operation is to divide by 3.
Two solutions: x = -8/3 and x = 8/3 since x^3 equations always have 2 solutions
One solution: x = -2 since (-2)^3 = -8
Two solutions: x = 2 and x = -2 since 2^3 = 8 and (-2)^3 = -8

Answer 2

The equation: x^2=25 will have how many solutions for x ?(1 point)
One solution: x = 25/2 since the inverse operation is to divide
Two solutions: x = 5 and x = -5 since 5^2 = 25 and also (-5)^2 = 25 and x^2 equations always have 2 solutions
One solution: x = 5 since 5^2 = 25
Two solutions: x = 25/2 and x = -25/2 since the inverse operation is division and x^2 equations always have 2 solutions

Answer 3

The equation: x^2=91 has what kind of solution(s) for x ?(2 points)
One rational, integer solution
One irrational solution
Two irrational solutions
Two rational, integer solutions

Answer 4

- Multiplication: Division
- x^3: Cube root (∛)
- √x: Square (x^2)
- Subtraction: Addition
- Addition: Subtraction
- Division: Multiplication
- x^2: Square root (√)

Answer 5

Two solutions: x = -2 since (-2)^3 = -8 and x = 2 since 2^3 = 8.

The equation x^3 = -8 will have two solutions, one for x = -2 and the other for x = 2, as both -2^3 = -8 and 2^3 = 8.

Answer 6

Two solutions: x = 5 since 5^2 = 25 and x = -5 since (-5)^2 = 25.

The equation x^2 = 25 will have two solutions, one for x = 5 and the other for x = -5, as both 5^2 = 25 and (-5)^2 = 25.

Answer 7

The equation x^2 = 91 has two irrational solutions.

To find the solutions, we need to take the square root of both sides of the equation:

x = ±√91

Since 91 is not a perfect square, the square root of 91 is an irrational number, and the equation x^2 = 91 will have two irrational solutions.