Question

solve equation for x. if the equation has a sloution that is in terms of other variables state any restrictions on tbose variables

Answer 1

Given the following equation:

`3\mleft(2-x\mright)-2\mleft(x+5\mright)=2-2\mleft(x-3\mright)`

You can solve for the variable "x" and find its value as follows:

1. Apply the Distributive Property on both sides of the equation:

`\begin{gathered} (3)\mleft(2)+(3)(-x\mright)+(-2)\mleft(x)+(-2)(5\mright)=2+(-2)\mleft(x)+(-2)(-3\mright) \\ 6-3x-2x-10=2-2x+6 \end{gathered}`

2. Add the like terms on both sides of the equation:

`-5x-4=8-2x`

3. Apply the Addition Property of Equality by adding 4 to both sides of the equation:

`\begin{gathered} -5x-4+(4)=8-2x+(4) \\ -5x=12-2x \end{gathered}`

4. Now apply the Addition Property of Equality by adding this term to both sides of the equation:

`2x`

As follows:

`\begin{gathered} -5x+(2x)=12-2x+(2x) \\ -3x=12 \end{gathered}`

5. Finally, you can apply the Division Property of Equality by dividing both sides of the equation by -3:

`\begin{gathered} (-3x)/(-3)=(12)/(-3) \\ \\ x=-4 \end{gathered}`

The answer is:

`x=-4`