Given the following equation:
[tex]3\mleft(2-x\mright)-2\mleft(x+5\mright)=2-2\mleft(x-3\mright)[/tex]
You can solve for the variable "x" and find its value as follows:
1. Apply the Distributive Property on both sides of the equation:
[tex]\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}[/tex]
2. Add the like terms on both sides of the equation:
[tex]-5x-4=8-2x[/tex]
3. Apply the Addition Property of Equality by adding 4 to both sides of the equation:
[tex]\begin{gathered} -5x-4+(4)=8-2x+(4) \\ -5x=12-2x \end{gathered}[/tex]
4. Now apply the Addition Property of Equality by adding this term to both sides of the equation:
[tex]2x[/tex]
As follows:
[tex]\begin{gathered} -5x+(2x)=12-2x+(2x) \\ -3x=12 \end{gathered}[/tex]
5. Finally, you can apply the Division Property of Equality by dividing both sides of the equation by -3:
[tex]\begin{gathered} \frac{-3x}{-3}=\frac{12}{-3} \\ \\ x=-4 \end{gathered}[/tex]
The answer is:
[tex]x=-4[/tex]
