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Subtract b from each side.

c. ax + b. =. c – b. ax. =. c – b. 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. Subtract b from each side.

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Subtract b from each side.

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  1. c ax + b = c – b ax = c – b 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. Assume a 0. Divide each side by a.

  2. for Example 1 GUIDED PRACTICE Solve the literal equation for x. Then use the solution to solve the specific equation 1.a – bx =c; 12 – 5x = –3

  3. for Example 1 GUIDED PRACTICE Solve the literal equation for x. Then use the solution to solve the specific equation 2.ax = bx + c; 11x = 6x + 20

  4. 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.

  5. GUIDED PRACTICE 3. Write 5x + 4y = 20 so that yis a function of x.

  6. The perimeter P ofa rectangle is given by the formula P =2l +2w where l is the length and w is the width. a. Solve the formula for the width w. 4 . for Examples 2 and 3 GUIDED PRACTICE

  7. The area Aof a triangle is given by the formula A = bhwhere bis the base and his the height. 1 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. EXAMPLE 3 Solve and use a geometric formula

  8. 5 9 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 = (F – 32) where Cis the temperature in degrees Celsius and Fis the temperature in degrees Fahrenheit.

  9. SOLUTION 9 9 5 9 5 9 5 5 9 5 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. C (F – 32) = 5 9 9 5 Multiply each side by , the reciprocal of . C = ·(F – 32) 9 C F – 32 = 5 32 Add to each side. = C + 32 F EXAMPLE 4 Solve a multi-step problem Write original formula. Simplify.

  10. 1 3 3. SolveV = BhforB. 1. Write the equation 15 = 5y – 4x so that y is a functionof x. 2. SolveC = 2prfor r.

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