# Manipulating Basic Linear Equations

The following is offered as a solution of the equation

-4[x-2(2x-3)]+1= 1/2(4x-6)

-4[x-2(2x-3)]+1=8x-12

-4x-4x+6+1=8x-12

-8x+7=8x-12

7= -12

Because 7 = -12 is not a true equation, the equation has no solution. If this is correct, state that there is no solution. If not, explain in detail why it is not correct, and supply the correct answer.

Finally, create an equation that includes at least one set of parentheses and one fraction that has a solution of -10.

#### Solution Preview

1) That equation actually does have a solution. The reason why is that you have a couple missteps in your simplification. This mostly comes from understanding how to apply parentheses. A good rule of thumb is to start from the innermost set of parentheses and work your way outward. Another important rule is that when you multiply things inside parentheses by a number, you have to multiply everything inside by that number. And finally, when you get to the point where you want to resolve the two sides of the equation, make sure you're doing exactly the same thing to the entirety of both sides.

I'm assuming that 1/2(4x-6) means one half (1/2), times (4x-6) (this is the most accurate, but some people might type that to mean 1 divided by the whole 2(4x-6)). So let's start. I'm going to do the left side first.

-4[x-2(2x-3)]+1= 1/2(4x-6)

-4[x-4x+6]+1= 1/2(4x-6)

Note that I multiplied both 2x and -3 by -2 (-2 times ...

#### Solution Summary

This solution shows the flaws in the analysis given in the question, how to avoid those mistakes, and how to solve the problem correctly. It also shows how to create an answer to the second question.