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Subtract b from each side.

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

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Subtract b from each side.

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  1. = c ax + b = c – b ax = c – b Assume a0. Divide each side by a. x = a EXAMPLE 1 Solve a literal equation Solve ax +b =cforx. Then use the solution to solve 2x + 5 = 11. SOLUTION Solve ax + b = cfor x. STEP 1 Write original equation. Subtract bfrom each side.

  2. x = = c – b 11– 5 = 3 a 2 The solution of2x + 5 = 11is 3. ANSWER EXAMPLE 1 Solve a literal equation Usethe solution to solve2x + 5 = 11. STEP 2 Solution of literal equation. Substitute 2 for a, 5 for b, and 11 for c. Simplify.

  3. = c a – bx = c – a – bx = a–c Assume b0. Divide each side by – 1. x = b for Example 1 GUIDED PRACTICE Solve the literal equation for x . Then use the solution to solve the specific equation 1.Solve a – bx =cforx. SOLUTION Solve a – bx = cfor x. STEP 1 Write original equation. Subtract afrom each side.

  4. x = 12– (–3) = 5 a – c = 3 b The solution of12 – 5x = –3is 3. ANSWER for Example 1 GUIDED PRACTICE Usethe solution to solve12 – 5x = –3. STEP 2 Solution of literal equation. Substitute a for 12, –3 for c, and 5for b. Simplify.

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

  6. c x = a – b 20 Substitute a for 11, 20 for c, and = 11 – 6 6for b. = 4 The solution of11x = 6x + 20. is 4. ANSWER for Example 1 GUIDED PRACTICE Usethe solution to solve11x = 6x + 20. STEP 2 Solution of literal equation. Simplify.

  7. 3 2 3x + 2y 8 = 2y 8 – 3x = y = 4 – x EXAMPLE 2 Rewrite an equation Write 3x + 2y = 8 so that yis a function of x. Write original equation. Subtract 3xfrom each side. Divide each side by 2.

  8. The area Aof a triangle is given by the formula A = bhwhere bis the base and his the height. 1 1 2 2 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. a. A bh = bh 2A = EXAMPLE 3 Solve and use a geometric formula SOLUTION Write original formula. Multiply each side by 2.

  9. 2A 2A = h b b b. Substitute 64.4 for Aand 14 for bin the rewritten formula. h = 2(64.4) = 14 ANSWER The height of the triangle is 9.2 meters. EXAMPLE 3 Solve and use a geometric formula Divide each side by b. Write rewritten formula. Substitute 64.4 for Aand 14 for b. =9.2 Simplify.

  10. 5 4 5x + 4y 20 = 4y 20 – 5x = y = 5 – x for Examples 2 and 3 GUIDED PRACTICE 3 . Write 5x + 4y = 20 so that yis a function of x. Write original equation. Subtract 5xfrom each side. Divide each side by 4.

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

  12. Substitute 19.2 for P and 7.2 for l in the rewritten formula b . 19.2 – 2 (7.2) = 2 w = p–2l 2 for Examples 2 and 3 GUIDED PRACTICE Write original equation. Substitute 19.2 for Pand 7.2 for l. = 2.4 Simplify. The width of the rectangle is 2.4 feet

  13. 5 9 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 =(F – 32) where Cis the temperature in degrees Celsius and F is the temperature in degrees Fahrenheit. EXAMPLE 4 Solve a multi-step problem Temperature

  14. 9 5 5 9 9 9 5 5 9 5 C (F –32) = 9 5 Multiply each side by , the reciprocal of . 9 5 C = . (F –32) 9 C F –32 = 5 32 Add to each side. = C + 32 F 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 Fis a function of C. Write original formula. Simplify.

  15. 9 5 The rewritten formula C + 32. = is F EXAMPLE 4 Solve a multi-step problem ANSWER

  16. 9 9 9 9 5 5 5 5 = F C +32 F C +32 = = (14)+32 =(10)+32 ANSWER ANSWER The low for Saturday is 57.2°F. The low for Sunday is 50°F. EXAMPLE 4 Solve a multi-step problem Find the low temperatures for Saturday and Sunday in degrees Fahrenheit. STEP 2 Saturday (lowof14°C) Sunday(low of10°C) =25.2 + 32 =18 + 32 = 57.2 = 50

  17. 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 Fis a function of C. for Example 4 GUIDED PRACTICE

  18. 9 9 5 9 5 9 9 5 5 5 5 9 C = . (F –32) = C + 32 F C (F –32) = The rewritten formula C + 32. = is F 5 9 Multiply each side by , the reciprocal of . 5 9 9 C F –32 = ANSWER 5 32 Add to each side. for Example 4 GUIDED PRACTICE Write original formula. Simplify.

  19. 9 9 9 9 5 5 5 5 = F C +32 F C +32 = =(22)+32 =(16)+32 ANSWER ANSWER The High for Saturday is 71.6°F. The High for Sunday is 60.8°F. for Example 4 GUIDED PRACTICE Find the high temperatures for Saturday and Sunday in degrees Fahrenheit. STEP 2 Saturday(Highof22°C) Sunday(High of16°C) =39.6 + 32 =28.8 + 32 = 71.6 = 60.8

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