Motivation Math Magic Choose a number.

DRILL Solve for x in each equation: 1)x + 13 = 20 2)x – 11 = -13 3)4x = 32

DRILL Solve for x in each equation: 1)x + 13 = 203) 4x = Divide by 4 x = 7 x = 8 2)x – 11 = x = - 2

Solving Two-Step Equations Algebra I Day 25

Solving Two-Step Equations To solve you must still isolate the variable by using opposite operations. When you have more than one step you must use the order of operations in reverse order. Ex: (add/subtract)(multiply/divide) (exponents)(parentheses)

Examples 1)2x + 5 = x = 12 Divide by 2 on both sides x = 6

DRILL Solve for x in each equation: 1)2x + 13 = 27 2)3x – 7 = -13 3)

Solve for x in each equation: 1)2x + 13 = x = 14 Divide both sides by 2 x = 7

Solve for x in each equation: 2) 3x – 7 = x = -6 Divide both sides by 3 x = -2

Solving Multi-Step Equations Algebra I Day 27

Combining Like-Terms Like terms are terms that have the exact same exponents and variables. When you add or subtract like terms you simply add/subtract the numbers in front of the variables (coefficients) and keep the variables and exponents the same.

Example 4x x – 2 = 33 7x + 5 = x = 28 Divide both sides by 7 x = 4

Distributive Property When you have a number (term) in parentheses next to an expression you must multiply the number (term) out front with each part of the expression inside the parentheses. Ex: 2(3x + 4) = 6x + 8

Examples 1)2(x + 5) = 34 2x + 10 = x = 24 Divide by 2 on both sides x = 12

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Contents Lesson 1-1Expressions and Formulas Lesson 1-2Properties of Real Numbers Lesson 1-3Solving Equations Lesson 1-4Solving Absolute Value Equations Lesson 1-5Solving Inequalities Lesson 1-6Solving Compound and Absolute Value Inequalities

Lesson 3 Contents Example 1Verbal to Algebraic Expression Example 2Algebraic to Verbal Sentence Example 3Identify Properties of Equality Example 4Solve One-Step Equations Example 5Solve a Multi-Step Equation Example 6Solve for a Variable Example 7Apply Properties of Equality Example 8Write an Equation

Example 3-1a Write an algebraic expression to represent 3 more than a number. Answer:

Example 3-1b Write an algebraic expression to represent 6 times the cube of a number. Answer:

Example 3-1c Write an algebraic expression to represent the square of a number decreased by the product of 5 and the same number. Answer:

Example 3-1d Write an algebraic expression to represent twice the difference of a number and 6. Answer:

Write an algebraic expression to represent each verbal expression. a. 6 more than a number b. 2 less than the cube of a number c. 10 decreased by the product of a number and 2 d. 3 times the difference of a number and 7 Example 3-1e Answer:

Example 3-2a Write a verbal sentence to represent. Answer: The sum of 14 and 9 is 23.

Example 3-2b Write a verbal sentence to represent. Answer: Six is equal to –5 plus a number.

Example 3-2c Write a verbal sentence to represent. Answer: Seven times a number minus 2 is 19.

Example 3-2d Write a verbal sentence to represent each equation. a. b. c. Answer: The difference between 10 and 3 is 7. Answer: Three times a number plus 2 equals 11. Answer: Five is equal to the sum of 2 and a number.

Example 3-3a Name the property illustrated by the statement if xy = 28 and x = 7, then 7y = 28. Answer: Substitution Property of Equality

Example 3-3b Name the property illustrated by the statement. Answer: Reflexive Property of Equality

Name the property illustrated by each statement. a. b. Answer: Transitive Property of Equality Example 3-3c Answer: Symmetric Property of Equality

Example 3-4a Solve. Check your solution. Original equation Add 5.48 to each side. Simplify. Check: Original equation Answer: The solution is 5.5. Simplify. Substitute 5.5 for s.

Example 3-4b Solve. Check your solution. Original equation Simplify. Multiply each side bythe multiplicative inverse of

Example 3-4c Answer: The solution is 36. Check: Original equation Simplify. Substitute 36 for t.

Solve each equation. Check your solution. a. b. Example 3-4d Answer: –2 Answer: 15

Example 3-5a Solve Original equation Distributive and Substitution Properties Commutative, Distributive, and Substitution Properties Addition and Substitution Properties Division and Substitution Properties Answer: The solution is –19.

Example 3-5b Answer: –6 Solve

Example 3-6a Geometry The area of a trapezoid is where A is the area, b 1 is the length of one base, b 2 is the length of the other base, and h is the height of the trapezoid. Solve the formula for h.

Example 3-6b Area of a trapezoid Multiply each side by 2. Simplify. Divide each side by. Simplify.

Example 3-6c Answer:

Example 3-6d Geometry The perimeter of a rectangle is where P is the perimeter, is the length, and w is the width of the rectangle. Solve the formula for w. w Answer:

Example 3-7a Multiple-Choice Test Item what is the value of AB CD

Example 3-7b Read the Test Item You are asked to find the value of the expression 4g – 2. Your first thought might be to find the value of g and then evaluate the expression using this value. However, you are not required to find the value of g. Instead, you can use the Subtraction Property of Equality on the given equation to find the value of 4g – 2.

Example 3-7c Solve the Test Item Original equation Subtract 7 from each side. Answer: B

Example 3-7d Multiple-Choice Test Item what is the value of A 12 B 6 C –6 D –12 Answer: D

Example 3-8a Home Improvement Carl wants to replace the 5 windows in the 2nd-story bedrooms of his home. His neighbor Will is a carpenter and he has agreed to help install them for $250. If Carl has budgeted $1000 for the total cost, what is the maximum amount he can spend on each window? Explore Let c represent the cost of each window. Plan The number of windows times the cost per window plus the cost for a carpenter equals the total cost. 5c+250=1000

Example 3-8b Solve Original equation Subtract 250 from each side. Simplify. Answer: Carl can afford to spend $ 150 on each window. Divide each side by 5.

Example 3-8c ExamineThe total cost to replace five windows at $150 each is 5(150) or $750. Add the $250 cost of the carpenter to that, and the total bill to replace the windows is or $1000. Thus, the answer is correct.

Home Improvement Kelly wants to repair the siding on her house. Her contractor will charge her $300 plus $150 per square foot of siding. How much siding can she repair for $1500? Example 3-8d Answer: 8 ft 2

End of Lesson 3