Clear your desk except for paper/pencil 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: Warm-up Use the equality properties to solve for a specified variable. Independent practice

Warm-up Which of the following equations have the correct solution? Select all that apply. 2𝑥 + 5 = 19; 𝑥 = 7 3 + 𝑥 + 2 − 𝑥 = 16; 𝑥 = 3 𝑥+2 5 =2; 𝑥 = 8 6 = 2𝑥 − 8; 𝑥 = 7 14 = 1 3 𝑥 + 5; 𝑥 = 18 Check: 2(7) + 5 = 19 Check: 3 + 3 + 2 – 3 = 16 Check: 8 + 2 5 =2 Check: 6 = 2(7) – 8 Check: 14 = 1 3 𝑥 + 5

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

Literal equations … ex. y = mx + b or P = 2L + 2W 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. 2w + 23 = 30 1. 2w + 2L = P for w w = 30 – 23 w = 302 w = w = P – 2L   w = 7 2 w = P – L w = 2

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

3. 2c – 10 + c = 8 2c-17 3. 3a + 3h – c = A for h 6 2c – 10 + c = 56 3a + 3h – c = 6A 3c – 10 = 56 h = 6 3 𝐴 – 3 3 𝑎 + 𝑐 3 c = 56 + 10 c = 56.3 h = 2𝐴 –𝑎 + 𝑐 3 c = 22

Solve for the indicated variable 5 4 𝑦+ 5 4 = 𝑥 5𝑦+5 = 4𝑥 𝑦 = 4 5 𝑥 – 5 5 𝑦 = 4 5 𝑥 – 1

Solve for the indicated variable How many factors? 3.

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Sports To find a baseball pitcher’s earned run average (ERA), you can use the formula Ei = 9r, 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 = 9r 9r. i E = Page 71

Meteorology For altitudes up to 36,000 feet, the relationship between ground temperature and atmospheric temperature can be described by the formula t = -0.0035a + 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 = g = a. temp. ∘F t = -0.0035a + g, Altitude (ft) g. temp. ∘F t – g . 0.0035 a =

17 people can attend the party Multi-Step The formula c = 5p + 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 = p = Cost in $ c = 5p + 215 People attending p = c – 215 5 300 – 215 5 Page 72 p = 17 people can attend the party

The cost c to be a member at the local gym is represented by the equation c = 30 + 3m, where m is the monthly cost. Write an expression to represent the monthly cost. 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 + 0.05s dollars. Write the equation in terms of her sales. What does the 1500 represent? c = 30 + 3m m = 𝑐 −30 3 I = 1500 + .05s s = 𝐼 −1500 0.5 The 150 represents her base salary

Matching worksheet follows

The cost c to be a member at the local gym is represented by the equation c = 30 + 3m, where m is the monthly cost. Write an expression to represent the monthly cost. 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 + 0.05s dollars. Write the equation in terms of her sales. What does the 1500 represent? Sports To find a baseball pitcher’s earned run average (ERA), you can use the formula Ei = 9r, 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. Meteorology For altitudes up to 36,000 feet, the relationship between ground temperature and atmospheric temperature can be described by the formula t = -0.0035a + 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. Multi-Step The formula c = 5p + 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?