EXAMPLE 1 Solve a literal equation Solve ax

EXAMPLE 1 Solve a literal equation Solve ax +b = c for x. Then use the solution to solve 2 x + 5 = 11. SOLUTION STEP 1 Solve ax + b = c for x. ax + b = c ax = c – b c–b x= a Write original equation. Subtract b from each side. Assume a = 0. Divide each side by a.

EXAMPLE 1 Solve a literal equation STEP 2 Use the solution to solve 2 x + 5 = 11. c–b x = a 11 – 5 = 2 =3 ANSWER Solution of literal equation. Substitute 2 for a, 5 for b, and 11 for c. Simplify. The solution of 2 x + 5 = 11 is 3.

GUIDED PRACTICE for Example 1 Solve the literal equation for x. Then use the solution to solve the specific equation 1. Solve a – bx = c for x. SOLUTION STEP 1 Solve a – bx = c for x. a – bx = c Write original equation. – bx = c – a Subtract a from each side. a–c x= b Assume b = 0. Divide each side by – 1.

GUIDED PRACTICE for Example 1 STEP 2 Use the solution to solve 12 – 5 x = – 3. a–c x = b 12 – (– 3) = 5 =3 ANSWER Solution of literal equation. Substitute a for 12, – 3 for c, and 5 for b. Simplify. The solution of 12 – 5 x = – 3 is 3.

GUIDED PRACTICE 2. for Example 1 Solve a x = bx + c for x. SOLUTION STEP 1 Solve a x = bx + c for x. a x = bx + c Write original equation. a x – bx = c c x= a–b Subtract bx from each side. Assume a = 0. Divide each side by a – b.

GUIDED PRACTICE for Example 1 STEP 2 Use the solution to solve 11 x = 6 x + 20. c x =a–b 20 = 11 – 6 =4 ANSWER Solution of literal equation. Substitute a for 11, 20 for c, and 6 for b. Simplify. The solution of 11 x = 6 x + 20. is 4.

EXAMPLE 2 Rewrite an equation Write 3 x + 2 y = 8 so that y is a function of x. 3 x + 2 y = 8 – 3 x y= 4– 3 x 2 Write original equation. Subtract 3 x from each side. Divide each side by 2.

EXAMPLE 3 Solve and use a geometric formula 1 The area A of a triangle is given by the formula A = bh 2 where b is the base and h is the height. a. Solve the formula for the height h. b. Use the rewritten formula to find the height of the triangle shown, which has an area of 64. 4 square meters. SOLUTION a. 1 A = 2 bh 2 A = bh Write original formula. Multiply each side by 2.

EXAMPLE 3 Solve and use a geometric formula 2 A =h b b. Divide each side by b. Substitute 64. 4 for A and 14 for b in the rewritten formula. 2 A h= b 2(64. 4) = 14 = 9. 2 ANSWER Write rewritten formula. Substitute 64. 4 for A and 14 for b. Simplify. The height of the triangle is 9. 2 meters.

GUIDED PRACTICE 3. for Examples 2 and 3 Write 5 x + 4 y = 20 so that y is a function of x. 5 x + 4 y = 20 – 5 x y= 5– 5 x 4 Write original equation. Subtract 5 x from each side. Divide each side by 4.

GUIDED PRACTICE 4. for Examples 2 and 3 The perimeter P of a rectangle is given by the formula P = 2 l + 2 w where l is the length and w is the width. a. Solve the formula for the width w. SOLUTION a. p = 2 l + 2 w Write original equation. p – 2 l = 2 w Subtract 2 l from each side. p – 2 l =w 2 Divide each side by 2.

GUIDED PRACTICE for Examples 2 and 3 b. Substitute 19. 2 for P and 7. 2 for l in the rewritten formula p – 2 l w= 2 19. 2 – 2 (7. 2) = 2. 4 Write original equation. Substitute 19. 2 for P and 7. 2 for l. Simplify. The width of the rectangle is 2. 4 feet

EXAMPLE 4 Solve a multi-step problem Temperature You are visiting Toronto, Canada, over the weekend. A website gives the forecast shown. Find the low temperatures for Saturday and Sunday in degrees Fahrenheit. Use the formula C = 5 (F – 32) where C is 9 the temperature in degrees Celsius and F is the temperature in degrees Fahrenheit.

EXAMPLE 4 Solve a multi-step problem SOLUTION STEP 1 Rewrite the formula. In the problem, degrees Celsius are given and degrees Fahrenheit need to be calculated. The calculations will be easier if the formula is written so that F is a function of C. 5 Write original formula. C = 9 (F – 32) 9 5 9 C =. (F – 32) 5 9 C = F – 32 5 9 C + 32 = F 5 9 Multiply each side by , the 5 reciprocal of 5. 9 Simplify. Add 32 to each side.

EXAMPLE 4 Solve a multi-step problem ANSWER 9 The rewritten formula is F = C + 32. 5

EXAMPLE 4 STEP 2 Solve a multi-step problem Find the low temperatures for Saturday and Sunday in degrees Fahrenheit. Saturday (low of 14°C) 9 F = C + 32 5 9 = 5 (14)+ 32 Sunday (low of 10°C) 9 F = C + 32 5 9 = 5 (10)+ 32 = 25. 2 + 32 = 18 + 32 = 57. 2 = 50 ANSWER The low for Saturday is 57. 2°F. The low for Sunday is 50°F.

GUIDED PRACTICE for Example 4 5. Use the information in Example 4 to find the high temperatures for Saturday and Sunday in degrees Fahrenheit. STEP 1 Rewrite the formula. In the problem, degrees Celsius are given and degrees Fahrenheit need to be calculated. The calculations will be easier if the formula is written so that F is a function of C.

GUIDED PRACTICE for Example 4 5 C = 9 (F – 32) 9 5 9 C =. (F – 32) 5 9 C = F – 32 5 9 C + 32 =F 5 Write original formula. 9 Multiply each side by , the 5 reciprocal of 5. 9 Simplify. Add 32 to each side. ANSWER 9 The rewritten formula is F = C + 32. 5

GUIDED PRACTICE STEP 2 for Example 4 Find the high temperatures for Saturday and Sunday in degrees Fahrenheit. Saturday (High of 22°C) 9 F = C + 32 5 9 = 5 (22)+ 32 = 39. 6 + 32 = 71. 6 Sunday (High of 16°C) 9 F = C + 32 5 9 = 5 (16)+ 32 = 28. 8 + 32 = 60. 8 ANSWER The High for Saturday is 71. 6°F. The High for Sunday is 60. 8°F.