Question

4x + 2(x – 3) = 4x + 2x – 11Part A: Solve the equation and write the number of solutions. Show all the steps. Part B: Name one property you used to solve this equation.

Answer 1

Part A:

The given equation is:

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

Combine like terms:

`4x+2(x-3)=6x-11`

Using the distributive property, expand the expression:

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

Combine like terms:

`6x-6=6x-11`

Using the Substitution Property of Equality, it follows that:

`\begin{gathered} 6x-6x-6=6x-6x-11 \\ -6=-11 \end{gathered}`

Since the statement -6 = -11 is false, it follows that there is no solution to the equation

Therefore, the number of solutions is 0

Part B: One property used is the Subtraction Property of Equality