Chapter 1 Section 3 ALGEBRA 2 Example

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Chapter 1 Section 3 ALGEBRA 2

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

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

Write an algebraic expression to represent 6 times the cube of a number. Answer:

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

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 Answer: c. 10 decreased by the product of a number and 2 d. 3 times the difference of a number and 7 Answer:

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

Write a verbal sentence to represent Answer: Six is equal to – 5 plus a number. .

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

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

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

Name the property illustrated by the statement. Answer: Reflexive Property of Equality

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

Solve . Check your solution. Original equation Add 5. 48 to each side. Simplify. Check: Original equation Substitute 5. 5 for s. Simplify. Answer: The solution is 5. 5.

Solve . Check your solution. Original equation Multiply each side by multiplicative inverse of Simplify. the

Check: Original equation Substitute 36 for t. Simplify. Answer: The solution is 36.

Solve each equation. Check your solution. a. Answer: b. – 2 Answer: 15

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.

Solve Answer: – 6

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.

Area of a trapezoid Multiply each side by 2. Simplify. Divide each side by Simplify. .

Answer:

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

Multiple-Choice Test Item what is the value of A B C D

Read the Test Item You are asked to find the value of the expression 4 g – 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 4 g – 2.

Solve the Test Item Original equation Subtract 7 from each side. Answer: B

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

Home Improvement Carl wants to replace the 5 windows in the 2 nd-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 the cost of windows times per window 5 c plus the cost for a carpenter + 250 the total equals cost. = 1000

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

Examine The 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 750 Thus, the answer is correct. + 250 or $1000.

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? Answer: 8 ft 2

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