Hi, there--

THE PROBLEM:
Solve for y. 
-4y + 10 = -2(3y + 1)

A SOLUTION:
We want to write a series of equivalent equations using the properties of equality to get this equation in
a "y equals something" form.

First, use the distributive property to clear the parentheses. We multiply -2 by each term in the 
parentheses.
-4y + 10 = -2(3y + 1)
-4y + 10 = -6y - 2

We would like all the terms on the left hand side, so add 6y to both sides. 
-4y + 10 + 6y = -6y - 2 + 6y

Combine the y-terms on each side. On the left, -4y+6y is 2y. On the right -6y+6y is 0.
2y + 10 = -2

We want all the constant terms on the right hand side, so we subtract 10 from both sides.
2y + 10 - 10 = -2 - 10

Combine like terms on each side. On the left, 10-10 is 0. On the right -2-10 is -12.
2y = -12

We know the 2 times y equals -12. We want to know what y equals, so we divide each side by 2.
2y/2 = -12/2

Simplify. On the left, 2y divided by 2 is y. On the right, -12/2 is -6.
y = -6

It is a good habit to check you work by substituting -6 for y in the original equation.
-4y + 10 = -2(3y + 1)
-4(-6) + 10 = -2(3(-6) + 1)

Simplify.
On the left, we have -4(-6) is 24. On the right, inside the parentheses, 3(-6) is -18.
24 + 10 = -2(-18 + 1)

On the left, 24+10 is 34. On the right, inside the parentheses, -18+1 is -17.
34 = -2(-17).

On the right, -2(-17) is 34.
34 = 34.

When you check your work, this how you want things to work out...a number equal to the same number.
This tells us that when y = -6, both sides of the equation have the same value,so the equation is true.


Hope this helps! Feel free to email if you have ANY questions about the solution.

Good luck with your math,

Mrs. F
math.in.the.vortex@gmail.com