Solving Equations With Variables On Both Sides
Solving Equations With Variables On Both Sides
What if there are variables on both sides of the equation? For equations like this, begin as we did above—choose a “variable” side and a “constant” side, and then use the subtraction and addition properties of equality to collect all variables on one side and all constants on the other side.
Example
Solve: \(9x=8x-6.\)
Solution
Here the variable is on both sides, but the constants only appear on the right side, so let’s make the right side the “constant” side. Then the left side will be the “variable” side.
| We don’t want any \(x\)’s on the right, so subtract the \(8x\) from both sides. | ||
| Simplify. | ||
| We succeeded in getting the variables on one side and the constants on the other, and have obtained the solution. | ||
| Check: | ||
| Let \(x=-6\). | ||
Example
Solve: \(5y-9=8y.\)
Solution
The only constant is on the left and the \(y\)’s are on both sides. Let’s leave the constant on the left and get the variables to the right.
| Subtract \(5y\) from both sides. | ||
| Simplify. | ||
| We have the y’s on the right and the constants on the left. Divide both sides by 3. |
||
| Simplify. | ||
| Check: | ||
| Let \(y=-3.\) | ||
Example
Solve: \(12x=\text{−}x+26.\)
Solution
The only constant is on the right, so let the left side be the “variable” side.
| Remove the \(-x\) from the right side by adding \(x\) to both sides. | |
| Simplify. | |
| All the \(x\)’s are on the left and the constants are on the right. Divide both sides by 13. | |
| Simplify. |
This lesson is part of:
Solving Linear Equations II