Algebra 1-6 Study Guide: Solving for a Variable (pp 49-51) Page! 1 of! 8. Vocabulary
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1 Page 1 of 8 Attendance Problems: Solve each equation x = m = 43 c = s = k - 6 = 9k + 2 formula Vocabulary literal equation I can solve a formula for a given variable. I can solve an equation in two or more variables for one of the variables. Common Core CC.9-12.A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. * CC.9-12.A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. CC.9-12.N.Q.1 Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.*
2 Page 2 of 8 6. What is a formula? In the formula d = rt, d is isolated. You can "rearrange" a formula to isolate any variable by using inverse operations. This is called solving for a variable. Solving for a Variable Step 1 Locate the variable you are asked to solve for in the equation. Step 2 Identify the operations on this variable and the order in which they are applied. Step 3 Use inverse operations to undo operations and isolate the variable.
3 Page 3 of 8 Video Example 1: In 2005, Cheri Blauwet was the top woman wheelchair finisher of the Boston Marathon with a time of about hours. The race was about 26.2 miles. What was her average speed? Use the formula d = rt and round your answer to the nearest tenth. 1 Sports Application In 2004, Ernst Van Dyk won the wheelchair race of the Boston Marathon with a time of about 1.3 hours. The race was about 26.2 miles. What was his average speed? Use the formula d = rt and round your answer to the nearest tenth. The question asks for speed, so first solve the formula d = rt for r. d = rt d t = rt t d_ t = r, or r = _ d t Locate r in the equation. Since r is multiplied by t, divide both sides by t to undo the multiplication. Now use this formula and the information given in the problem. r = _ d t _ Van Dyk s average speed was about 20.2 miles per hour.
4 Page 4 of 8 Example 1: The formula C = πd gives the circumference of a circle C in terms of diameter d. The circumference of a bowl is 18 inches. What is the bowl's diameter? Leave the symbol π in your answer. 7. Guided Practice: Solve the formula d = rt for t. Find the time in hours that it would take Ernst Van Dyk to travel 26.2 miles if his average speed was 18 miles per hour. Video Example 2: The formula C = 5 gives the 9 F 32 Celsius temperature C in terms of F. Solve for F. Remember ( ) Dividing by a fraction is the same as multiplying by the reciprocal.
5 Page 5 of 8 Example 2: A. The formula for the area of a triangle is A = 1, where b is the 2 bh 2 Solving Formulas for a Variable A The formula for a Fahrenheit temperature in terms of degrees Celsius C Solve for C. is F = 9 5 F = _ 9 C + 32 Locate C in the equation. 5 Since 32 is added to 9 C, subtract 32 from both sides to undo the addition. F - 32 = _ 9 5 C _ ( 5 9 ) (F - 32) = _ ( 5 _ 9 ) 9 5 C 5_ (F - 32) = C 9 length of the base, and h is the height. Solve for h. Since C is multiplied by 9, divide both 5 sides by 9 5 (multiply by 5 9) to undo the multiplication. B The formula for a person s typing speed is s = w - 10e m, where s is speed in words per minute, w is number of words typed, e is number of errors, and m is number of minutes typing. Solve for w. w - 10e s = _ Locate w in the equation. m Since w - 10e is divided by m, multiply both m (s) = m ( w _ - m 10e ) sides by m to undo the division. ms = w - 10e Since 10e is subtracted from w, add 10e to + 10e + 10e ms + 10e = w both sides to undo the subtraction.
6 Page 6 of 8 B. The formula for a person s typing speed is s = w 10e where m, s is speed in words per minute, w is number of words typed, e is number of errors, and m is number of minutes typing. Solve for e. 8. Guided Practice: The formula for an object s final velocity is f = i gt, where i is the object s initial velocity, g is acceleration due to gravity, and t is time. Solve for i. 9. What is a literal equation? Video Example 3: A. Solve 3t + 4z = 5 for t.
7 Page 7 of 8 B. Solve PV = RST for T. 3 Solving Literal Equations for a Variable A Solve m - n = 5 for m. m - n = 5 Locate m in the equation. + n + n m = 5 + n B Solve _ m = x for k. k m_ k = x k ( m _ k ) = kx m = kx m x = kx x m_ x = k Since n is subtracted from m, add n to both sides to undo the subtraction. Locate k in the equation. Since k appears in the denominator, multiply both sides by k. Since k is multiplied by x, divide both sides by x to undo the multiplication. Example 3. A. Solve x + y = 15 for x. _
8 Page 8 of 8 B. Solve pq = x for q. Guided Practice. 10. Solve 5 b = 2t for t. 11. Solve D = m for V. V 1-6 Solving for a Variable: (pp 52-53) 8, 9, 11, 13, 24, 28, 30,
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= ( 17) = (-4) + (-6) = (-3) + (- 14) + 20
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