1. Introduction
Literal equations are equations that involve two or more variables. Sometimes it is useful to rearrange or solve literal equations for a specific variable in order to find a solution to a given problem. In this lesson, literal equations and formulas, or literal equations that state specific rules or relationships among quantities, will be examined.
1.5.1: Rearranging Formulas

2. Key Concepts
It is important to remember that both literal equations and formulas contain an equal sign indicating that both sides of the equation must remain equal.
Literal equations and formulas can be solved for a specific variable by isolating that variable.
1.5.1: Rearranging Formulas

3. Key Concepts, continued
To isolate the specified variable, use inverse operations. When coefficients are fractions, multiply both sides of the equation by the reciprocal. The reciprocal of a number, also known as the inverse of a number, can be found by flipping a number.
1.5.1: Rearranging Formulas

4. Key Concepts, continued
Think of an integer as a fraction with a denominator of 1. To find the reciprocal of the number, flip the fraction. The number 2 can be thought of as the fraction To find the reciprocal, flip the fraction: becomes . You can check if you have the correct reciprocal because the product of a number and its reciprocal is always 1.
1.5.1: Rearranging Formulas

5. Common Errors/Misconceptions
solving for the wrong variable
improperly isolating the specified variable by using the opposite inverse operation
incorrectly simplifying terms
1.5.1: Rearranging Formulas

6. Guided Practice Example 3 Solve 4y + 3x = 16 for y.
1.5.1: Rearranging Formulas

7. Guided Practice: Example 3, continued
Begin isolating y by subtracting 3x from both sides of the equation.
1.5.1: Rearranging Formulas

8. ✔ Guided Practice: Example 3, continued
To further isolate y, divide both sides of the equation by the coefficient of y.
The coefficient of y is 4. Be sure that each term of the equation is divided by 4. ✔
1.5.1: Rearranging Formulas

9. Guided Practice: Example 3, continued
1.5.1: Rearranging Formulas

10. Guided Practice Example 4
The formula for finding the area of a triangle is , where b is the length of the base and h is the height of the triangle. Suppose you know the area and height of the triangle, but need to find the length of the base. In this case, solving the formula for b would be helpful.
1.5.1: Rearranging Formulas

11. Guided Practice: Example 4, continued
Begin isolating b by multiplying both sides of the equation by the reciprocal of , or 2.
1.5.1: Rearranging Formulas

12. Guided Practice: Example 4, continued
Multiplying both sides of the equation by the reciprocal is the same as dividing both sides of the equation by . The result will be the same.
1.5.1: Rearranging Formulas

13. Guided Practice: Example 4, continued
To further isolate b, divide both sides of the equation by h. or
1.5.1: Rearranging Formulas

14. ✔ Guided Practice: Example 4, continued
The formula for finding the length of the base of a triangle can be found by doubling the area and dividing the result by the height of the triangle. ✔
1.5.1: Rearranging Formulas

15. Guided Practice: Example 4, continued
1.5.1: Rearranging Formulas