Question

How do you solve `2( x + 5) = 2x + 6- 3x`?

Answer 1

You simplify, and then use what my math teacher calls the "balancing property".

Explanation:

2(x + 5) simplifies to 2x + 10 by the distributive property, making the equation 2x + 10 = 2x + 6 - 3x.

2x + 6 - 3x simplifies to -x + 6, because 2x - 3x = -x.

What my math teacher calls the "balancing property" is basically the idea that in algebra, what you do to anything on one side of an equal sign, you have to do to the other. In other words, if you add x to one side, you have to add x to the other.

Using that example, we can do that for this equation.
2x + 10 = -x + 6
+x +x
= =
3x + 10 = 6

Then, we can use the same property to subtract 10 from both sides.

3x + 10 = 6
-10 -10
3x = -4

We can use this property a third time, to divide both sides by 3.

`(3x)/3 = (-4)/3`

x = `-4/3`, or -1.3333333333333333333...