Solving Linear Equations Chapter 1

Solving Simple Equations and Multi-Step Equations I can solve multi-step linear equations using inverse operations.

Solving Simple Equations and Multi-Step Equations Vocabulary (page 4 in Student Journal) equation: a statement that 2 expressions are equal linear equation in one variable: an equation that can be written in the form ax + b = 0, where a and b are constants and a cannot equal 0 solution: a value that makes the equation true

Solving Simple Equations and Multi-Step Equations inverse operations: operations that undo each other (i.e. addition and subtraction) equivalent equations: equations with the same solution(s)

Solving Simple Equations and Multi-Step Equations Core Concepts (pages 4 and 5 in Student Journal) Addition Property of Equality if a = b, then a + c = b + c Subtraction Property of Equality if a = b, then a - c = b - c

Solving Simple Equations and Multi-Step Equations Multiplication Property of Equality if a = b, then ac = bc Division Property of Equality if a = b, then a/c = b/c

Solving Simple Equations and Multi-Step Equations Examples (space on page 9 in Student Journal) Solve the following equations. m - 8 = -14 b) 19 = r/3

Solving Simple Equations and Multi-Step Equations Solutions m = -6 b) r = 57

Solving Simple Equations and Multi-Step Equations Solve the following equations. c) 11m - 8 - 6m = 22 d) 18 = 3(2x - 6)

Solving Simple Equations and Multi-Step Equations Solutions c) m = 6 d) x = 6

Solving Simple Equations and Multi-Step Equations Write and solve an equation for the situation. e) A 160 pound delivery person uses an elevator to bring 50 pound boxes up to an office. If the elevator has a maximum capacity of 1000 pounds, how many boxes can the delivery person put bring up at one time?

Solving Simple Equations and Multi-Step Equations Solution e) 160 + 50b = 1000 b = 16.8 16 boxes

Solving Equations with Variables on Both Sides I can solve linear equations that have variables on both sides.

Solving Equations with Variables on Both Sides Vocabulary (page 14 in Student Journal) identity: an equation that is true for every possible value of the variable

Solving Equations with Variables on Both Sides Core Concepts (pages 14 and 14 in Student Journal) In order to solve equations with variables on both sides of the equals sign we can follow the steps below 1. use the Distributive Property to remove any grouping symbols 2. combine like terms to simplify both sides of the equation

Solving Equations with Variables on Both Sides 3. get the variable terms on one side of the equation and the constant terms on the other side of the equation using the properties of equality 4. use the properties of equality to solve for the variable 5. check your solution An equation that is not true for any value of the variable has no solution.

Solving Equations with Variables on Both Sides Examples (space of pages 14 and 15 in Student Journal) a) 7k + 2 = 4k - 10 b) 2(5x - 1) = 3(x + 11)

Solving Equations with Variables on Both Sides Solutions a) k = -4 b) x = 5

Solving Equations with Variables on Both Sides c) One music download store charges $10 a month plus $1 per song. Another store charges $20 a month and $0.50 per song. How many songs can you download so that the price is the same for both stores?

Solving Equations with Variables on Both Sides Solution c) 10 + 1s = 20 + .5s, s = 20 so 20 songs

Solving Equations with Variables on Both Sides d) 3(4b - 2) = -6 + 12b e) 2x + 7 = -1(3 - 2x)

Solving Equations with Variables on Both Sides Solutions d) 12b - 6 = 12b - 6, identity e) 2x + 7 = 2x - 3, no solution

Solving Absolute Value Equations I can solve absolute value equations.

Solving Absolute Value Equations Vocabulary (page 19 in Student Journal) absolute value equation: an equation that contains an absolute value expression extraneous solution: an apparent solution that must be rejected because it does not satisfy the original equation

Solving Absolute Value Equations Examples (space on page 20 in Student Journal) abs(x + 6) = 11 abs(3x – 6) – 9 = -3 abs(2m + 5) = abs(m) abs(3n + 18) = 6n

Solving Absolute Value Equations Solutions x = 5 and x = -17 x = 0 and x = 4 m = -5 and m = -5/3 n = 6 (n = -2 is extraneous and should be rejected)

Rewriting Equations and Formulas I can rewrite literal equations.

Rewriting Equations and Formulas Vocabulary (page 24 in Student Journal) literal equation: an equation that involves 2 or more variables formula: a special type of literal equation that states a relationship among 2 or more variables

Rewriting Equations and Formulas Examples (space on page 24 in Student Journal) Solve the following literal equations and formulas for the given variable. a) -t = r + px, for p b) C = 5/9(F - 32)

Rewriting Equations and Formulas Solutions a) (-t - r)/x = p b) 9/5C + 32 = F