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**10-5 Solving for a Variable Warm Up Problem of the Day**

Course 3 Warm Up Problem of the Day Lesson Presentation

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**Solving for a Variable 10-5 Warm Up Solve. 1. 8x – 9 = 23**

Course 3 10-5 Solving for a Variable Warm Up Solve. 1. 8x – 9 = 23 2. 9x + 12 = 4x + 37 3. 6x – 8 = 7x + 3 4. x + 3 = x = 4 x = 5 x = –11 1 2 1 8 23 4 x = – , or –5 3

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**Solving for a Variable 10-5 Problem of the Day**

Course 3 10-5 Solving for a Variable Problem of the Day The formula A = 4r2 gives the surface area of a geometric figure. Solve the formula for r. Can you identify what the geometric figure is? sphere

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**Solving for a Variable Learn to solve an equation for a variable. 10-5**

Course 3 10-5 Solving for a Variable Learn to solve an equation for a variable.

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**Solving for a Variable 10-5**

Course 3 10-5 Solving for a Variable If an equation contains more than one variable, you can sometimes isolate one of the variables by using inverse operations. You can add and subtract any variable quantity on both sides of an equation.

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**Solving for a Variable 10-5**

Course 3 10-5 Solving for a Variable Additional Example 1A: Solving for a Variable by Addition or Subtraction Solve for the indicated variable. A. Solve a – b + 1 = c for a. a – b + 1 = c Add b and subtract 1 from both sides. + b – b – 1 a = c + b – 1 Isolate a.

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**Solving for a Variable 10-5**

Course 3 10-5 Solving for a Variable Additional Example 1B: Solving for a Variable by Addition or Subtraction Solve for the indicated variable. B. Solve a – b + 1 = c for b. a – b + 1 = c Subtract a and 1 from both sides. – a – – a – 1 –b = c – a – 1 Isolate b. –1 (–b) = –1 (c – a – 1) Multiply both sides by –1. b = –c + a + 1 Isolate b.

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**Solving for a Variable 10-5 Try This: Example 1A**

Course 3 10-5 Solving for a Variable Try This: Example 1A Solve for the indicated variable. A. Solve y – b + 3 = c for y. y – b + 3 = c Add b and subtract 3 from both sides. + b – b – 3 y = c + b – 3 Isolate y.

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**Solving for a Variable 10-5 Try This: Example 1B**

Course 3 10-5 Solving for a Variable Try This: Example 1B Solve for the indicated variable. B. Solve p – w + 4 = f for w. p – w + 4 = f Subtract p and 4 from both sides. – p – – p – 4 –w = f – p – 4 Isolate w. –1 (–w) = –1 (f – p – 4) Multiply both sides by –1. w = –f + p + 4 Isolate w.

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**Solving for a Variable 10-5**

Course 3 10-5 Solving for a Variable To isolate a variable, you can multiply or divide both sides of an equation by a variable if it can never be equal to 0. You can also take the square root of both sides of an equation that cannot have negative values.

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**Solving for a Variable 10-5**

Course 3 10-5 Solving for a Variable Additional Example 2A: Solving for a Variable by Division or Square Roots Solve for the indicated variable. Assume all values are positive. A. Solve A = s2 for s. A = s2 √A = √s2 Take the square root of both sides. √A = s Isolate s.

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**Solving for a Variable 10-5**

Course 3 10-5 Solving for a Variable Additional Example 2B: Solving for a Variable by Division or Square Roots Solve for the indicated variable. Assume all values are positive. B. Solve V = IR for R. V = IR = Divide both sides by I. IR I V I V = R Isolate R.

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**Solving for a Variable 10-5**

Course 3 10-5 Solving for a Variable Additional Example 2C: Solving for a Variable by Division or Square Roots C. Solve the formula for the area of a trapezoid for h. Assume all values are positive. A = h(b1 + b2) 1 2 Write the formula. 2 • A = 2 • h(b1 + b2) 1 2 Multiply both sides by 2. 2A = h(b1 + b2) 2A (b1 + b2) h(b1 + b2) = Divide both sides by (b1 + b2). 2A (b1 + b2) = h Isolate h.

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**Solving for a Variable 10-5 Try This: Example 2A**

Course 3 10-5 Solving for a Variable Try This: Example 2A Solve for the indicated variable. Assume all values are positive. A. Solve w = g2 + 4 for g. w = g2 + 4 – – 4 Subtract 4 from both sides. w – 4 = g2 Take the square root of both sides. √w – 4 = √g2 √ w – 4 = g Isolate g.

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**Solving for a Variable 10-5 Try This: Example 2B**

Course 3 10-5 Solving for a Variable Try This: Example 2B Solve for the indicated variable. Assume all values are positive. B. Solve A = lw for w. A = lw = Divide both sides by l. lw l A l A = w Isolate w.

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**Solving for a Variable 10-5 Try This: Example 2C**

Course 3 10-5 Solving for a Variable Try This: Example 2C Solve for the indicated variable. Assume all values are positive. C. Solve s = 180(n – 2) for n. s = 180(n – 2) s (n – 2) 180 = Divide both sides by 180. s 180 = (n – 2) + 2 + 2 Add 2 to both sides. s 180 + 2 = n

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**Solving for a Variable 10-5 Remember!**

Course 3 10-5 Solving for a Variable To find solutions (x, y), choose values for x substitute to find y. Remember!

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**Additional Example 3: Solving for y and Graphing**

Course 3 10-5 Solving for a Variable Additional Example 3: Solving for y and Graphing Solve for y and graph 3x + 2y = 8. 3x + 2y = –3x –3x x y 2y = –3x + 8 –2 7 4 –3x + 8 2 2y = 2 1 y = –3x 2 4 –2

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**Additional Example 3 Continued**

Course 3 10-5 Solving for a Variable Additional Example 3 Continued 3x + 2y = 8

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**Solving for a Variable 10-5 Try This: Example 3**

Course 3 10-5 Solving for a Variable Try This: Example 3 Solve for y and graph 4x + 3y = 12. 4x + 3y = x y –4x – 4x –3 8 3y = –4x + 12 4 –4x + 12 3 3y = 3 6 –4 y = –4x 3

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**Try This: Example 3 Continued**

Course 3 10-5 Solving for a Variable Try This: Example 3 Continued y 10 8 6 4x + 3y = 12 4 2 x –4 – –2 –4 –6

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**Insert Lesson Title Here**

Course 3 10-5 Solving for a Variable Insert Lesson Title Here Lesson Quiz: Part 1 Solve for the indicated variable. 1. P = R – C for C. 2. P = 2l+ 2w for l. 3. V = Ah for h. 4. R = for S. C = R - P = l P – 2w 2 = h 3V A 1 3 C – S t C – Rt = S

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**Insert Lesson Title Here**

Course 3 10-5 Solving for a Variable Insert Lesson Title Here Lesson Quiz: Part 2 5. Solve for y and graph 2x + 7y = 14. y = – 2x 7

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