Literal Equations (2-8) Objective: Solve equations for given variables. Use formulas to solve real-world problems.

Solve for a Specific Variable Some equations contain more than one variable. At times, you will need to solve these equations for one of the variables.

Example 1 Solve 5b + 12c = 9 for b. 5b + 12c = 9 -12c -12c 5 5

Solve for a Specific Variable. Sometimes we need to solve equations for a variable that is on both sides of the equation. When this happens, you must get all terms with that variable onto one side of the equation. It is then helpful to use the Distributive Property to isolate the variable for which you are solving.

Example 2 Solve 7x – 2z = 4 – xy for x. 7x – 2z = 4 – xy +2z +2z 7x = 4 – xy + 2z +xy +xy 7x + xy = 4 + 2z x(7 + y) = 4 + 2z 7 + y 7 + y

Use Formulas A formula or equation that involves several variables is called a literal equation. To solve a literal equation, apply the process of solving for a specific variable.

Example 3 A car’s fuel economy E (miles per gallon) is given by the formula E = m/g, where m is the number of miles driven and g is the number of gallons of fuel used. Solve the formula for m. g • • g Eg = m m = Eg

Example 3 A car’s fuel economy E (miles per gallon) is given by the formula E = m/g, where m is the number of miles driven and g is the number of gallons of fuel used. If Qhanah’s car has an average fuel consumption of 30 miles per gallon and she used 9.5 gallons, how far did she drive? m = Eg = 30(9.5) = 285 miles

Dimensional Analysis When using formulas, you may want to use dimensional analysis. Dimensional analysis or unit analysis is the process of carrying units throughout a computation.

Example 4 The average weight of the chimpanzees at a zoo is 52 kilograms. If 1 gram ≈ 0.0353 ounce, use dimensional analysis to find the average weight of the chimpanzees in pounds. (Hint: 1 lb = 16 oz) 52 kg ≈ 115 lbs

Check Your Progress Choose the best answer for the following. Solve 2x – 17y = 13 for y. y = y = 2x + 4 2x – 17y = 13 -2x -2x -17y = 13 – 2x -17 -17

Check Your Progress Choose the best answer for the following. Solve 12a + 3c = 2ab + 6 for a. a = 12a + 3c = 2ab + 6 -3c -3c 12a = 2ab + 6 – 3c -2ab -2ab 12a – 2ab = 6 – 3c a(12 – 2b) = 6 – 3c 12 – 2b 12 – 2b

Check Your Progress Choose the best answer for the following. A car’s fuel economy E (miles per gallon) is given by the formula E = m/g, where m is the number of miles driven and g is the number of gallons of fuel used. Solve the formula for g. g = mE m = gE g = Eg = m E E

Check Your Progress Choose the best answer for the following. Janet is walking 20 laps of a track in a relay to raise money for cancer research. If each lap is 350 meters, how many miles will Janet walk? (Hint: 1 meter ≈ 1.094 yards and 1 mile = 1760 yards) about 4.35 mi about 7 mi about 7.7 mi about 8 mi 20 laps