Algebraic Expressions and Operations

The video tutorial explains how to translate verbal statements into algebraic expressions using the variable x. It covers two examples: one involving addition and the other multiplication. The first example translates 'the sum of a number increased by three and the number decreased by 20' into an algebraic expression. The second example translates 'the product of twice a number and seven more than five times a number' into an expression. The tutorial emphasizes understanding terms like 'sum' and 'product' and how they relate to algebraic operations.

What variable is used to represent the unknown number in the algebraic expressions?

• a

• x

• z

• y

In the first example, what operation is indicated by the word 'sum'?

• Multiplication

• Subtraction

• Division

• Addition

How is 'a number increased by three' represented in algebraic terms?

• x - 3

• x + 3

• 3x

• x/3

What is the algebraic expression for 'the number decreased by 20'?

• x + 20

• x - 20

• 20 - x

• 20 + x

What does the expression 'x + 3 + x - 20' simplify to?

• 2x - 17

• x + 23

• 2x + 17

• x - 23

In the second example, what does the term 'product' refer to?

• Subtraction

• Addition

• Multiplication

• Division

How is 'twice a number' expressed algebraically?

• 2 + x

• 2x

• x/2

• x - 2

What is the expression for 'five times a number'?

• x/5

• 5x

• 5 + x

• x - 5

How do you represent 'seven more than five times a number'?

• 5x + 7

• 7x + 5

• 7 - 5x

• 5 + 7x

What is the complete expression for 'the product of twice a number and seven more than five times a number'?

• 2x + 5x + 7

• 2x(5x + 7)

• 2(x + 5x + 7)

• 2x + 7(5x)