|Math Skills Review|
The key to solving simple algebraic equations containing a single unknown (e.g. x + 6 = 10) is to realize that the equation is an equality. As long as you do the same mathematical operation (e.g. add a constant, subtract a constant, multiply by a constant, and divide by a constant) to both sides of the equation, the equality is still an equality. This includes squaring both sides of the equation or taking the square root of both sides of the equation.
|Example 1||To solve for x, it is necessary to subtract 6 from both sides of the equation|
|Example 2||To solve for x, you need to add 6 to both sides of the equation and then divide both sides by 2.|
|Example 3||To isolate x, you need to|
(1) multiply through by 6,
(2) subtract 2 from both sides, and
(3) divide both sides by 5.
|Example 4||To solve for x this time, you need to|
(1) multiply both sides of the equation by 4 and 3 to cancel out the denominator in line 2,
| Example 4|
|This process is called "cross-multiplying." This entails multiplying the numerator of one side of the equality by the denominator of the other side of the equality. When this is done, the very same line 3 results. The rest of the problem is done identically.|
|Example 5||This problem could be very complicated and become a quadratic equation. However, because it has a perfect square on both sides, if you simply take the square root of both sides of the equality, you are left in line 3 with a straightforward algebra problem as you solve for the positive root, which I did here.
In Chemistry, when we use this technique to solve equilibrium problems, only one of the roots is meaningful. Of course, the square root of 49 can be -7 as well as +7. You can then go ahead and solve for the second root, x = -0.8 = -4/5.
QUIZ: Solve for x.
|Question 1||Question 2||Question 3||Question 4|
|Dimensional Analysis||Significant Figures||Manipulation of Exponents|
|Scientific Notation||Logarithms||The Quadratic Equation|