Question

solve the equation and check.
\\(-3(2y - 6) - y = -2(y - 4)\\)

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
\\(\boldsymbol{\odot}\\) a. the solution is \\(2\\).
\\(\quad\\) (type an integer or a simplified fraction.)
\\(\boldsymbol{\circ}\\) b. the solution is all real numbers.
\\(\boldsymbol{\circ}\\) c. there is no solution.

Explanation:

Step1: Expand both sides

Left side: $-3(2y - 6)-y=-6y + 18 - y=-7y + 18$
Right side: $-2(y - 4)=-2y + 8$
So the equation becomes $-7y + 18=-2y + 8$

Step2: Move terms with y to left

Add $2y$ to both sides: $-7y + 2y+ 18=-2y + 2y+ 8$
Simplify: $-5y + 18 = 8$

Step3: Move constants to right

Subtract 18 from both sides: $-5y + 18 - 18= 8 - 18$
Simplify: $-5y=-10$

Step4: Solve for y

Divide both sides by -5: $y=\frac{-10}{-5}=2$

Check:

Left side: $-3(2*2 - 6)-2=-3(4 - 6)-2=-3*(-2)-2 = 6 - 2 = 4$
Right side: $-2(2 - 4)=-2*(-2)=4$
Left = Right, so y=2 is correct.

Answer:

A. The solution is 2.