Question

Help of you can.

An equation is shown below:

4x + 2(x − 3) = 4x + 2x − 11

Part A: Solve the equation and write the number of solutions. Show all the steps. (6 points)

Part B: Name one property you used to solve this equation. (4 points)

Answer 1

Part A. Couldn't find a variable to solve for.

This equation is invalid, the left and right sides are not equal, therefore there is no solution.

Part B. Distributive Property

Explanation:

Simplifying

4x + 2(x + -3) = 4x + 2x + -11

Reorder the terms:

4x + 2(-3 + x) = 4x + 2x + -11

4x + (-3 * 2 + x * 2) = 4x + 2x + -11

4x + (-6 + 2x) = 4x + 2x + -11

Reorder the terms:

-6 + 4x + 2x = 4x + 2x + -11

Combine like terms: 4x + 2x = 6x

-6 + 6x = 4x + 2x + -11

Reorder the terms:

-6 + 6x = -11 + 4x + 2x

Combine like terms: 4x + 2x = 6x

-6 + 6x = -11 + 6x

Add '-6x' to each side of the equation.

-6 + 6x + -6x = -11 + 6x + -6x

Combine like terms: 6x + -6x = 0

-6 + 0 = -11 + 6x + -6x

-6 = -11 + 6x + -6x

Combine like terms: 6x + -6x = 0

-6 = -11 + 0

-6 = -11

Solving

-6 = -11

Couldn't find a variable to solve for.

This equation is invalid, the left and right sides are not equal, therefore there is no solution.

Answer 2

Part A: No Solution

Part B: Distributive Property

Explanation:

4x + 2x - 6 = 6x - 11

6x - 6 = 6x - 11

-6 ≠ -11

No Solution