1. Lesson 3-8 Solving Equations and Formulas

4. Objectives Solve equations for given variables Use formulas to solve real-world problems

5. Vocabulary Dimensional analysis – process of carrying units throughout a computation Literal equation – an equation that consists mostly of variables (formulas are literal equations)

6. Four-Step Problem Solving Plan Step 1: Explore the Problem –Identify what information is given (the facts) –Identify what you are asked to find (the question) Step 2: Plan the Solution –Find an equation the represents the problem –Let a variable represent what you are looking for Step 3: Solve the Problem –Plug into your equation and solve for the variable Step 4: Examine the Solution –Does your answer make sense? –Does it fit the facts in the problem?

7. Example 1 Solve for b. Simplify. Subtract 12c from each side. Divide each side by 5. or Simplify. Answer: The value of b is.

8. Example 2 Solve for x. Original equation Simplify. Use the Distributive Property Add xy to each side. Add 2z to each side.

9. Example 2 cont Answer: The value of x is. Since division by 0 is undefined,. Divide each side by 7 + y.

10. Example 3 Fuel Economy A car’s fuel economy E (miles per gallon) is given by the formula, where m is the number of miles driven and g is the number of gallons of fuel used. Solve the formula for m. Formula for fuel economy. Simplify.Answer: Multiply each side by g.

11. Example 4 Geometry The formula for the volume of a cylinder is, where r is the radius of the cylinder and h is the height. Solve the formula for h. Original formula Answer: Divide each side by.

12. Example 5 Geometry What is the height of a cylindrical swimming pool that has a radius of 12 feet and a volume of 1810 cubic feet? Answer:The height of the cylindrical swimming pool is about 4 feet. Formula for h V = 1810 and r = 12 Use a calculator.

13. Summary & Homework Summary: –For equations with more than one variable, you can solve for one of the variables by using the same steps as solving equations with one variable Homework: –pg 168: 14-30 even