Question

An equation is shown below: 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

$\begin{gathered} 4x+2(x-3)=4x+2x-11 \\ \end{gathered}$

Part A:

Use distributive property on the left hand side:

$\begin{gathered} 4x+2x-6=4x+2x-11 \\ \end{gathered}$

Add like terms:

$6x-6=6x-11$

Add 6 to both sides:

$\begin{gathered} 6x-6+6=6x-11+6 \\ 6x=6x-5 \end{gathered}$

Subtract 6x from both sides:

$\begin{gathered} 6x-6x=6x-6x-5 \\ 0=-5 \\ False \end{gathered}$

Therefore, the equation has no solution

Part B:

Addition Property of Equality

If two expressions are equal to each other, and you add the same value to both sides of the equation, the equation will remain equal.