Question

Simplify the following expression.(3x-5)-4(x-2)

Answer 1

Given the expression:

`\mleft(3x-5\mright)-4\mleft(x-2\mright)`

You need to remember the following:

- The Sign Rules for Multiplication:

`\begin{gathered} +\cdot+=+ \\ -\cdot-=+ \\ -\cdot+=- \\ +\cdot-=- \end{gathered}`

- The Distributive Property:

`\begin{gathered} a(b+c)=ab+ac \\ \\ a(b-c)=ab-ac \end{gathered}`

Then, the steps to simplify the expression are:

1. Apply the Distributive Property:

`\begin{gathered} =(3x-5)-(4)(x)+(4)(2) \\ =3x-5-4x+8 \end{gathered}`

2. Finally, add the like terms:

`=-x+3`

Therefore, the answer is:

`-x+3`