Question

Translate each of the following into an expression or equation:

1. The sum of a number and 5 is 20
2. Ten more than a number
3. A number increased by eleven is twenty one
4. Three times a number increased by 4
5. The sum of a five times a number and six
6. Seven more than three times a number
7. The difference between ten times a number and 3
8. Subtract eight from six times and number
9. Eight less than a number is five
10. Five times a number decreased by six
11. A number decreased by seven
12. The product of a number and seven
13. The sum of twice a number and four
14. The quotient of a number and three
15. A number divided by eleven

Answer 1

Verbal statements can be precisely translated into algebraic expressions and equations using mathematical operations and a variable, typically represented as 'x'. The translation involves identifying and applying operations such as addition, subtraction, multiplication, and division.

Step-by-step explanation:

Translating Statements into Algebraic Expressions and Equations

Translating verbal statements into algebraic expressions and equations is fundamental in algebra. Let's define a variable, let's say x, to represent the unknown number in each statement provided. Here's how we translate each of the provided statements into an expression or equation:

The sum of a number and 5 is 20: x + 5 = 20

Ten more than a number: x + 10

A number increased by eleven is twenty one: x + 11 = 21

Three times a number increased by 4: 3x + 4

The sum of five times a number and six: 5x + 6

Seven more than three times a number: 3x + 7

The difference between ten times a number and 3: 10x - 3

Subtract eight from six times a number: 6x - 8

Eight less than a number is five: x - 8 = 5

Five times a number decreased by six: 5x - 6

A number decreased by seven: x - 7

The product of a number and seven: 7x

The sum of twice a number and four: 2x + 4

The quotient of a number and three: x / 3

A number divided by eleven: x / 11

This exercise involves using different operations such as addition, multiplication, and subtraction to form expressions and equations, reflecting the various ways in which these operations can be combined with numbers and variables. Note the use of parentheses to clarify operations when necessary.

Answer 2

You have to translate these sentences into expressions. I am not going to solve all of these because if I explain one/two problems to you, you'll get the hang of it. Seven more than three times a number: 7+3x; Five times a number decreased by six: 5x-6

Step-by-step explanation:

Why? We don't know what number that is, so we can put any variable like (x, y, z, a, b, etc.). Three times a number is simply that number times 3. In this case we would input: 3*x, or 3x. 7 more than that number is 3x+7. Five times a number decreased by six: 5x-6 . Remember: it is simply 5*x which simplifies to 5x. Decreased is take away, so take away 6, and get 5x-6

Key words: Quotient: the result after dividing two/or more numbers; Product: the result after multiplying two/ or more numbers; Decreased: take away (Example: x decreased by 7=x-7)

I hope you understand!! It is very simple after you start to get the hang of it!!