Question

How can you transform the equation 8x - 10 + 10 + 4x = -10 + 6x + 6x + 10 into the form of a = a, where a is a number, to show that the equation has an infinite number of solutions? Select all that apply.

A. by adding 12x to both sides of the equation and then simplifying

B. by subtracting 8x to both sides of the equation and then simplifying

C. by subtracting 12x from both sides of the equation then simplifying

D. by subtracting 20 from both sides of the equation then simplifying

E. by dividing 6x from both sides of the equation and then simplifying

Answer 1

Explanation:

Simplifying

8x + -10 + 10 + 4x = -10 + 6x + 6x + 10

Reorder the terms:

-10 + 10 + 8x + 4x = -10 + 6x + 6x + 10

Combine like terms: -10 + 10 = 0

0 + 8x + 4x = -10 + 6x + 6x + 10

8x + 4x = -10 + 6x + 6x + 10

Combine like terms: 8x + 4x = 12x

12x = -10 + 6x + 6x + 10

Reorder the terms:

12x = -10 + 10 + 6x + 6x

Combine like terms: -10 + 10 = 0

12x = 0 + 6x + 6x

12x = 6x + 6x

Combine like terms: 6x + 6x = 12x

12x = 12x

Add '-12x' to each side of the equation.

12x + -12x = 12x + -12x

Combine like terms: 12x + -12x = 0

0 = 12x + -12x

Combine like terms: 12x + -12x = 0

0 = 0

Solving

0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

Simplifying

8x + -10 + 10 + 4x = -10 + 6x + 6x + 10

Reorder the terms:

-10 + 10 + 8x + 4x = -10 + 6x + 6x + 10

Combine like terms: -10 + 10 = 0

0 + 8x + 4x = -10 + 6x + 6x + 10

8x + 4x = -10 + 6x + 6x + 10

Combine like terms: 8x + 4x = 12x

12x = -10 + 6x + 6x + 10

Reorder the terms:

12x = -10 + 10 + 6x + 6x

Combine like terms: -10 + 10 = 0

12x = 0 + 6x + 6x

12x = 6x + 6x

Combine like terms: 6x + 6x = 12x

12x = 12x

Add '-12x' to each side of the equation.

12x + -12x = 12x + -12x

Combine like terms: 12x + -12x = 0

0 = 12x + -12x

Combine like terms: 12x + -12x = 0

0 = 0

Solving

0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.