1 Clear your desk except for paperpencil 2

1) Clear your desk except for paper/pencil 2) Copy the DATE and TOPIC Date: August 7(22) TOPIC : Solve for a specified variable in a literal equation ESSENTIAL QUESTION: How does solving a literal equation compare/contrast to solving a one-variable equation? AGENDA: 1. Warm-up 2. Use the equality properties to solve for a specified variable. 3. Independent practice

Warm-up Check: 2(7) + 5 = 19 Check: 3 + 2 – 3 = 16 Check: 6 = 2(7) – 8

Review 1. 3(2 x + 40) – 2 = 5 x – 5 6 x + 120 – 2 = 5 x – 5 6 x + 118 = 5 x – 5 x + 118 = -5 x = -123 2. 3 x + 4 = 7 4 5 15 x + 80 = 28 x = -52/15 3. 5 x – 6 = -7 3 5 x – 6 = -21 x = -3 4. 5 x + 2 = 10 3 x – 1 = 6 30 x + 12 = 30 x – 10 12 = -10 no solution

Literal equations … ex. y = mx + b or P = 2 L + 2 W • are solved like “regular” equations. • The answer to a one-variable equation is a value • The answer to a literal equation is an expression. • are solved by isolating for a specified variable. • are like formulas where there is more than one variable. • most useful when using a graphing calculator

Steps to solve any equation 1. Parenthesis 2. Fractions 3. Combine like terms 4. Combine variable terms of both sides. (cross the border) 5. Solve. (B. O. D. ) Regular equation Literal equation Solve for the variable Solve for the indicated variable 1. 2 w + 23 = 30 1. 2 w + 2 L = P for w w = 30 – 23 w = P – 2 L w = 302 w = 7 2 w = P – L w = 2

2. 3(2 + c) = 8 7 6 + 3 c = 56 – 6 c = 563 c = 50 3 2. h(a + c) = A for c 4 ah + ch = A 4 ah + ch = 4 A c = 4 A – ah c = 1 h h c = 4 A – a c = h

3. 2 c – 10 + c = 8 2 c-17 2 c – 10 + c = 56 3 c – 10 = 56 c = 56 + 10 c = 56. 3 c = 22 3. 3 a + 3 h – c = A 6 3 a + 3 h – c = 6 A for h

Solve for the indicated variable •

Solve for the indicated variable How many factors? 3.

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11. Sports To find a baseball pitcher’s earned run average (ERA), you can use the formula Ei = 9 r, in which E represents ERA, i represents the number of innings pitched, and r represents the number of earned runs allowed. Solve the equation for E. Ei = 9 r E= 9 r. i

12. Meteorology For altitudes up to 36, 000 feet, the relationship between ground temperature and atmospheric temperature can be described by the formula t = -0. 0035 a + g, in which t is the atmospheric temperature in degrees Fahrenheit, a is the altitude, in feet, at which the atmospheric temperature is measured, and g is the ground temperature in degrees Fahrenheit. Solve the equation for a. t = a. temp. ∘F a = Altitude (ft) g = g. temp. ∘F t = -0. 0035 a + g, a= t–g. 0. 0035

13. Multi-Step The formula c = 5 p + 215 relates c, the total cost in dollars of hosting a birthday party at a skating rink, to p, the number of people attending. If Allie’s parents are willing to spend $300 for a party, how many people can attend? c = Cost in $ p = People attending c = 5 p + 215 p = c – 215 5 p= 300 – 215 5 17 people can attend the party

14. The cost c to be a member at the local gym is represented by the equation c = 30 + 3 m, where m is the monthly cost. Write an expression to represent the monthly cost. 15. A car sales lady makes both a base salary and also a commission, which is a percentage of what she sells each month. if her sales total s dollars, her income I = 1500 + 0. 05 s dollars. Write the equation in terms of her sales. What does the 1500 represent?

Matching worksheet follows

11. Sports To find a baseball pitcher’s earned run average (ERA), you can use the formula Ei = 9 r, in which E represents ERA, i represents the number of innings pitched, and r represents the number of earned runs allowed. Solve the equation for E. 12. Meteorology For altitudes up to 36, 000 feet, the relationship between ground temperature and atmospheric temperature can be described by the formula t = -0. 0035 a + g, in which t is the atmospheric temperature in degrees Fahrenheit, a is the altitude, in feet, at which the atmospheric temperature is measured, and g is the ground temperature in degrees Fahrenheit. Solve the equation for a. 13. Multi-Step The formula c = 5 p + 215 relates c, the total cost in dollars of hosting a birthday party at a skating rink, to p, the number of people attending. If Allie’s parents are willing to spend $300 for a party, how many people can attend? 14. The cost c to be a member at the local gym is represented by the equation c = 30 + 3 m, where m is the monthly cost. Write an expression to represent the monthly cost. 15. A car sales lady makes both a base salary and also a commission, which is a percentage of what she sells each month. if her sales total m dollars, she makes a total of 1500 + 0. 05 s dollars. Write the equation in terms of her sales. What does the 1500 represent?