There are a few rules to follow when solving algebraic equations.
1. Use the distributive property.
If there is any parentheses in your equations, you can simplify them with the distributive property.
a(b + c) = ab + ac
2. Combine like terms.
Make sure to combine all like terms on both sides of the equation.
3. Use The Addition Principle of Equality if needed.
The Addition Principle of Equality states that if you add an expression to both sides of the equation, you will get a second equation that is equivalent to the original equation. Or in other words, they will both have the same solution set.
4. Use The Multiplication or Division Principle of Equality if needed.
Similar to the above rule. If you multiply or divide both sides of an equation with the same expression, the resulting equation will have the same solution set as the original equation.
Now that I showed you the rules necessary to solve an algebraic equation, let's solve the one you asked us to solve.
-2(7 - y) + 4 = -4
I see parentheses and we can use the distributive property to get rid of them.
-2(7 - y) + 4 = -4
-14 + 2y + 4 = -4
On the left-hand side, we have like terms that we can combine.
-14 + 2y + 4 = -4
-10 + 2y = -4
Now use The Addition Principle of Equality by adding 10 to each side of the equation.
-10 + 2y + 10 = -4 + 10
2y = 6
Awesome! The -10 constant term disappeared on the left-hand side.
Finally, use The Multiplication or Division Principle of Equality.
Divide both sides by the coefficient of the term 2y.
2y / 2 = 6 / 2
y = 3
So, y is equal to 3.
