Content Standards

A.CED.1 Create equations and inequalities in one variable and use them to solve problems.

Mathematical Practices

3 Construct viable arguments and critiquethe reasoning of others.

8 Look for and express regularity in repeatedreasoning.

You used properties of real numbers to evaluate expressions.

• Translate verbal expressions into algebraic expressions and equations, and vice versa.

• Solve equations using the properties of equality.

• open sentence

• equation

• solution

Verbal to Algebraic Expression

A. Write an algebraic expression to represent the verbal expression 7 less than a number.

Answer:

Verbal to Algebraic Expression

A. Write an algebraic expression to represent the verbal expression 7 less than a number.

Answer: n – 7

Verbal to Algebraic Expression

B. Write an algebraic expression to represent the verbal expression the square of a number decreased by the product of 5 and the number.

Answer:

Verbal to Algebraic Expression

B. Write an algebraic expression to represent the verbal expression the square of a number decreased by the product of 5 and the number.

Answer: x2 – 5x

A. 6x

B. x + 6

C. x6

D. x – 6

A. Write an algebraic expression to represent the verbal expression 6 more than a number.

A. 6x

B. x + 6

C. x6

D. x – 6

A. Write an algebraic expression to represent the verbal expression 6 more than a number.

A. x3 – 2

B. 2x3

C. x2 – 2

D. 2 + x3

B. Write an algebraic expression to represent the verbal expression 2 less than the cube of a number.

A. x3 – 2

B. 2x3

C. x2 – 2

D. 2 + x3

B. Write an algebraic expression to represent the verbal expression 2 less than the cube of a number.

Algebraic to Verbal Sentence

A. Write a verbal sentence to represent 6 = –5 + x.

Answer:

Algebraic to Verbal Sentence

A. Write a verbal sentence to represent 6 = –5 + x.

Answer: Six is equal to –5 plus a number.

Algebraic to Verbal Sentence

B. Write a verbal sentence to represent 7y – 2 = 19.

Answer:

Algebraic to Verbal Sentence

B. Write a verbal sentence to represent 7y – 2 = 19.

Answer: Seven times a number minus 2 is 19.

A. The difference of a number and 3 is 7.

B. The sum of a number and 3 is 7.

C. The difference of 3 and a number is 7.

D. The difference of a number and 7 is 3.

A. What is a verbal sentence that represents the equation n – 3 = 7?

A. The difference of a number and 3 is 7.

B. The sum of a number and 3 is 7.

C. The difference of 3 and a number is 7.

D. The difference of a number and 7 is 3.

A. What is a verbal sentence that represents the equation n – 3 = 7?

A. Five is equal to the difference of 2 and a number.

B. Five is equal to twice a number.

C. Five is equal to the quotient of 2 and a number.

D. Five is equal to the sum of 2 and a number.

B. What is a verbal sentence that represents the equation 5 = 2 + x?

A. Five is equal to the difference of 2 and a number.

B. Five is equal to twice a number.

C. Five is equal to the quotient of 2 and a number.

D. Five is equal to the sum of 2 and a number.

B. What is a verbal sentence that represents the equation 5 = 2 + x?

Solve One-Step Equations

A. Solve m – 5.48 = 0.02. Check your solution.

m – 5.48 = 0.02 Original equation

m – 5.48 + 5.48 = 0.02 + 5.48 Add 5.48 to each side.

m = 5.5 Simplify.

Check m – 5.48 = 0.02 Original equation

Answer:

0.02 = 0.02 Simplify.

5.5 – 5.48 = 0.02 Substitute 5.5 for m.

?

Solve One-Step Equations

Original equation

Simplify.

Solve One-Step Equations

Answer:

Substitute 36 for t.

Simplify.

Check Original equation

?

A. –8

B. –2

C. 2

D. 8

A. What is the solution to the equation x + 5 = 3?

A. –8

B. –2

C. 2

D. 8

A. What is the solution to the equation x + 5 = 3?

B. What is the solution to the equation

A. 5

B.

C. 15

D. 30

B. What is the solution to the equation

A. 5

B.

C. 15

D. 30

Solve a Multi-Step Equation

Solve 53 = 3(y – 2) – 2(3y – 1).

53 = 3(y – 2) – 2(3y – 1) Original equation

53 = 3y – 6 – 6y + 2 Apply the Distributive Property.

53 = –3y – 4 Simplify the right side.

57 = –3y Add 4 to each side.

–19 = y Divide each side by –3.

Answer:

Solve a Multi-Step Equation

Solve 53 = 3(y – 2) – 2(3y – 1).

53 = 3(y – 2) – 2(3y – 1) Original equation

53 = 3y – 6 – 6y + 2 Apply the Distributive Property.

53 = –3y – 4 Simplify the right side.

57 = –3y Add 4 to each side.

–19 = y Divide each side by –3.

Answer: The solution is –19.

What is the solution to 25 = 3(2x + 2) – 5(2x + 1)?

A. –6

B.

C.

D. 6

What is the solution to 25 = 3(2x + 2) – 5(2x + 1)?

A. –6

B.

C.

D. 6

A B

C D

Read the Test ItemYou 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. Notice that you are not required to find the value of g. Instead, you can use the Subtraction Property of Equality.

Solve the Test Item

Answer:

Original equation

Subtract 7 from each side.

Simplify.

Solve the Test Item

Answer: C

Original equation

Subtract 7 from each side.

Simplify.

A. 12

B. 6

C. –6

D. –12

If 2x + 6 = –3, what is the value of 2x – 3?

A. 12

B. 6

C. –6

D. –12

If 2x + 6 = –3, what is the value of 2x – 3?