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Section 6.7 / Literal Equations 6.7 Objective A 327 Literal Equations To solve a literal equation for one of the variables A literal equation is an equation that contains more than one variable. Examples of literal equations are shown at the right. Formulas are used to express a relationship among physical quantities. A formula is a literal equation that states a rule about measurements. Examples of formulas are shown at the right. 2x 3y 6 4w 2x z 0 1 1 1 R1 R2 R s a n 1d A P Prt (Physics) (Mathematics) (Business) The Addition and Multiplication Properties can be used to solve a literal equation for one of the variables. The goal is to rewrite the equation so that the variable being solved for is alone on one side of the equation and all the other numbers and variables are on the other side. HOW TO Video Solve A P1 i for i. The goal is to rewrite the equation so that i is on one side of the equation and all other variables are on the other side. A P1 i A P Pi A P P P Pi A P Pi AP Pi P P • Use the Distributive Property to remove parentheses. • Subtract P from each side of the equation. • Divide each side of the equation by P. Copyright © Houghton Mifflin Company. All rights reserved. AP i P Example 1 You Try It 1 Solve 3x 4y 12 for y. Solve 5x 2y 10 for y. Solution Your solution 3x 4y 12 3x 3x 4y 3x 12 4y 3x 12 4y 3x 12 4 4 3 y x3 4 • Subtract 3x. • Divide by 4. Solution on p. S17 328 Chapter 6 / Rational Expressions Example 2 Solve I You Try It 2 E for R. Rr Solve s Solution AL for L. 2 Your solution E I Rr R rI R r E Rr RI rI E RI rI rI E rI RI E rI RI E rI I I E rI R I • Multiply by (R r). • Subtract rI. • Divide by I. Example 3 You Try It 3 Solve L a1 ct for c. Solve S a n 1d for n. Solution Your solution L a1 ct L a act L a a a act L a act La act at at La c at • Distributive Property • Subtract a. Example 4 You Try It 4 Solve S C rC for C. Solve S rS C for S. Solution Your solution S C rC S 1 rC S 1 rC 1r 1r S C 1r • Factor. • Divide by (1 r). Solutions on p. S18 Copyright © Houghton Mifflin Company. All rights reserved. • Divide by at. Section 6.7 / Literal Equations 329 6.7 Exercises Objective A To solve a literal equation for one of the variables For Exercises 1 to 15, solve for y. 1. 3x y 10 2. 2x y 5 3. 4x y 3 4. 5x y 7 5. 3x 2y 6 6. 2x 3y 9 7. 2x 5y 10 8. 5x 2y 4 9. 2x 7y 14 10. 6x 5y 10 11. x 3y 6 12. x 2y 8 14. y 4 2x 3 15. 2 y 1 x 6 3 16. x 3y 6 17. x 6y 10 18. 3x y 3 19. 2x y 6 20. 2x 5y 10 21. 4x 3y 12 22. x 2y 1 0 23. x 4y 3 0 24. 5x 4y 20 0 13. y 2 3x 2 Copyright © Houghton Mifflin Company. All rights reserved. For Exercises 16 to 24, solve for x. For Exercises 25 to 40, solve the formula for the given variable. 25. d rt; t (Physics) 26. E IR; R (Physics) 27. PV nRT; T (Chemistry) 28. A bh; h (Geometry) 330 Chapter 6 / Rational Expressions (Geometry) 30. F 9 C 32; C 5 1 hb1 b2; b1 2 (Geometry) 32. C 5 F 32; F 9 V 1 Ah; h 3 (Geometry) 34. P R C; C (Business) 35. R CS ;S t (Business) 36. P RC ;R n (Business) 37. A P Prt; P (Business) 38. T fm gm; m (Engineering) 39. A Sw w; w (Physics) 40. a S Sr; S (Mathematics) 29. P 2l 2w; l 31. A 33. (Temperature conversion) (Temperature conversion) APPLYING THE CONCEPTS Business Break-even analysis is a method used to determine the sales volume required for a company to break even, or experience neither a profit nor a loss on the sale of a product. The break-even point represents the number of units that must be made and sold for income from sales to equal the cost of the prodF , SV where F is the fixed costs, S is the selling price per unit, and V is the variable costs per unit. Use this information for Exercise 41. 41. a. Solve the formula B F SV for S. b. Use your answer to part a to find the selling price per unit required for a company to break even. The fixed costs are $20,000, the variable costs per unit are $80, and the company plans to make and sell 200 desks. c. Use your answer to part a to find the selling price per unit required for a company to break even. The fixed costs are $15,000, the variable costs per unit are $50, and the company plans to make and sell 600 cameras. Copyright © Houghton Mifflin Company. All rights reserved. uct. The break-even point can be calculated using the formula B