Solving+Linear+Equations+1B-1

__**The Balance Method**__
by: Marjorie

General Rules 1) We put all the variables on one side, and all constants on the other side. 2)In order to find X We divide the number that is next to X by the number on the other side.

o We find the L.C.M of 5,4,2,4 = 20, so we multiply everything by 20 so it allows us to created and easier expression. o We put all the variables on one side, and all constants on the other side. o In order to find x we divide 30 by 2.

math \frac{3}{5}x-\frac{3}{4}={1}{2}x+ \frac{3}{4} math

o We must find the L.C.M of 5,4,2,4 = 20, so we multiply everything by 20 so it allows us to created and easier expression. math 20(\frac{3}{5}x-\frac{3}{4})=20({1}{2}x+ \frac{3}{4}) math

Using the distributive property, we get the following. math \frac{60}{5}x-\frac{60}{4}=\frac{20}{2}x+ \frac{60}{4} math

Now we can simplify our equation and follow the **General Rules**: math 12x-15 = 10x + 15 math

math 12x-10x = 15 + 15 math

math 2x = 30 math

math x = \frac{30}{2} math

math x =15 math

For more information go to : [|math equation web site]

__**Checking Solutions**__
by: Brianna and Mr. Rochester

To check the solution to any equation you must first make sure that the value of both sides of your equation are equal when you substitute the value(s) for you unknown variable(s). Simply stated, once you have gotten an answer you need to plug in your solution to find out if the answer you got for x is correct.

math \frac{3}{5}x-\frac{3}{4}={1}{2}x+ \frac{3}{4} math
 * Example:**

To verify that the solution x= 15 is correct, we will plug it into our original equation and simplify both sides. math \frac{3}{5}(15)-\frac{3}{4}=\frac{1}{2}(15)+ \frac{3}{4} math

math 9-\frac{3}{4}=7.5+ \frac{3}{4} math

math 9-.75=7.5+ .75 math

math 8.25=8.25 math

Our solutions is correct because we obtained the value of 8.25 for each side when we plugged in x= 15 for both equations. If we did not obtain the same value for both sides, then that means a mistake was made somewhere and we would need to go back and fix it. If you show your work, your error will be easier to find.

edited by Mr. Rochester