Algebra II 1.3 Solving Equations

 In math, what are variables? Letters that represent numbers. Letters that represent numbers.  In math, what is an equation? A mathematical expression to include an equal sign. A mathematical expression to include an equal sign. Open sentence – a mathematical sentence containing one or more variables.

 Write an algebraic expression to represent each verbal expression.  1A) 7 less than a number.  x – 7  B) three times the square of a number.  3x²  C) the cube of a number increased by 4 times the same number.  x³ + 4x  D) twice the sum of a number and 5.  2 (x + 5)

 2A) 10 = 12 – 2  Ten is equal to twelve minus two.  B) n + (-8) = -9  The sum of a number and -8 is -9.  C) n/6 = n²  A number divided by six is equal to that  number squared.

Properties of Equality PropertySymbolsExamples Reflexive A = A -7 + n = -7 + n Symmetric If a= b, then b = a If 3 = 5x – 6, then 5x – 6 = 3 Transitive If a = b, and b = c, then a = c If 2x+1 = 7 and 7 = 5x -8, then 2x+1 = 5x-8 Substitution If a = b, then a can replace b If (4+5)m = 18, then 9m = 18

 Name the property illustrated.  3. 3m = 5n, and 5n = 10p, then 3m = 10p  Transitive property  4. If -11a + 2 = -3a, then -3a= -11a + 2  Symmetric property

Warmup 8/31/12  1. Write an example of the symmetric property.  2. Write an expression for 2(2x -6).

Problems  Solve these equations.  1. X + 14 = X = -21 X = -21  x = x = 42 3x = 42 x = 14 x = 14

 a – 5 = a = a = 2.7 a = 1.5 a = 1.5  4. -4(k + 7) = k - 28 = k - 28 = k = 16 -4k = 16 k = -4 k = -4

5. 7x + x – 3x = -24 5x = -24 5x = -24 x = -4.8 x = -4.8  6. 3d + 7 = 6d d -6d -6d -6d -3d + 7 = 5 -3d + 7 = d = -2 -3d = -2 d = 2/3 d = 2/3

Inequalities  Rules for Multiplication / Division –When you multiply / divide both sides by a negative, you must __________ the sign.  Try these and Graph on a number line:  1. a < 3.7  2. 5 ≥ 3x

Solving for a variable  Place a box around the number you are solving for. Move everything to the other side using equation rules.  Example1: Solve for r when d = rt  Example 2: Solve for h when V = ⅓iir²h

Inequalities  Rules for Multiplication / Division –When you multiply / divide both sides by a negative, you must flip the sign. Try these and graph on a number line:  1. a < a < 1.2 a < 1.2  2. 5 ≥ 3x 3x ≤ 5 3x ≤ 5 x ≤ 5/3 x ≤ 5/3

Solve and Graph  – 8n ≤ n ≤ n ≤ -14 n ≥ 7/4 n ≥ 7/4 4.2 (4t + 9) < 18 8t + 18 < 18 8t + 18 < t < 0 8t < 0 t < 0 t < 0

Warmup 9/4/12  1. Solve 4(x + 2) = 12  2. Solve and graph: 2x + 6 < 12

Word Problems 7. Austin and Anna go to the West Bladen Bowling alley. They have a total of $31 to spend on their bowling adventure. It costs $3.50 to rent shoes and $6.00 per game to bowl. Find the maximum number of games that they can bowl if they each rent shoes.  What information should the variable represent? The amount per game.  Write the equation for the word problem and solve. 31 = 6.00x x = 4 games

8. Suppose Brandon and Barbie also go to West Bladen Bowling alley but they have a total of $60 to spend on bowling. Find the maximum number of games that they can bowl if they rent shoes. Let n be the variable this time.  Write an equation for this word problem and solve. 60 = 6.00x x = 8 games 60 = 6.00x x = 8 games

9. Larry spent $10,734 on his living expenses last year. Most of these expenses are listed to the right. If he paid rent 12 times last year, how much was Larry’s rent each month? Expense Annual Cost Electric$622 Gas$428 Water$240 Renter’sInsurance$144

Assignment  In your workbook:  Do page 3 (13-26 all)  Do page 5 (1-16 all)  ***Remember to show ALL work!!!