Give an Equations with the variable on both sides ?
Many equations that you encounter will have variables on both sides. Some of these equations will even contain grouping symbols like parentheses.
To solve equations with the variable on both sides, be sure to follow the following steps:
1. Distribute when necessary, and then simplify both sides of the equation.
2. Eliminate the variable term from one of the sides of the equation.
3. Eliminate the non-variable term on the side with the variable next.
4. Eliminate the coefficient from the variable term last.
Let's run through some examples where these steps are needed to solve the equations. Solve the following for the unknown variable:
Example 1:
13 - 8x = 5x + 2 (Add 8x to both sides, to eliminate the
13 - 8x + 8x = 5x + 8x+ 2 variable term on the left side)
13 = 13x + 2
13 - 2 = 13x + 2 - 2
11 = 13x
1.gif (252 bytes)
2.gif (146 bytes)= x
Now you may be thinking, "Does it matter which side?" you eliminate the variable term from?
Well, lets go ahead and solve the same equation by eliminating the 5x term instead.
13 - 8x = 5x + 2 (Subtract 5x from both sides, to eliminate
13 - 8x - 5x = 5x - 5x + 2 the variable term on the right side)
13 - 13x = 2
13 - 13 - 13x = 2 - 13
- 13x = -11
3.gif (285 bytes)
x = 2.gif (146 bytes)
Notice that the solution is the same either way that you solve it.
Important: It doesn't matter which side of the equation you eliminate the variable from, you will always get the same answer!