Question

Solve the equation 4(x + 2) = 3x + 4 algebraically. Show your work.

Answer 1

We have to solve the equation

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

By clearing the variable x. As we see the x+2 inside a parenthesis, and a 4 at the side, we will use the distributive property, and we will multiply number 4 by each of the elements inside the parenthesis, as shown:

`4x+8=3x+4`

Now, we will clear the variable x, we start by substracting an 8 to both sides of the equation:

`\begin{gathered} 4x+8-8=3x+4-8 \\ 4x+0=3x-4 \\ 4x=3x-4 \end{gathered}`

Lastly, we will substract a 3x to both sides, so we can disappear the 3x that is on the right side.

`4x-3x=3x-4-3x`

We make the substraction on the first side, and we use the commutative (order of summands doesn't change the result) and the modulative property (a number added with its opposite is equal to zero).

`\begin{gathered} 1x=3x-3x-4 \\ x=0-4 \\ x=-4 \end{gathered}`

Which means the solution of our equation is x=-4.