Question

Write an algebraic expression to represent each verbal expression.

1. four times the sum of a number and 3

2. 7 less than fifteen times a number

3. the difference of nine times a number and the quotient of 6 and the same number

4. the sum of 100 and four times a number

5. the product of 3 and the sum of 11 and a number

6. four times the square of a number increased by five times the same number

7. 23 more than the product of 7 and a number

Answer 1

Question (1):
Assume that the number is x
We want to get: four times the sum of x and 3
This means that we would add x and 3 first and then multiply the result by 4.
The algebraic expression would be as follows:
4(x+3)

Question (2):
Assume that the number is x.
We want to get: 7 less than fifteen times x
This means that we would multiply the x by 15 and then subtract 7 from the product.
The algebraic expression would be as follows:
15x - 7

Question (3):
Assume that the number is x.
We want to get: the difference of nine times x and the quotient of 6 and x 
This means that:
i- We would first multiply 9 by the number x
ii- Then we would divide 6 by x
iii- Finally we will subtract the quotient (step ii) from the product (step i)
The algebraic expression would be as follows:
(9x) - (6/x)

Question (4):
Assume that the number is x.
We want to get: the sum of 100 and four times a number
This meas that we would first multiply 4 by x and then add 100 to the product.
The algebraic expression would be as follows:
4x + 100

Question (5):
Assume that the number is x.
We want to get: the product of 3 and the sum of 11 and x
This means that we would first add 11 to the number x and then multiply the result by 3
The algebraic expression would be as follows:
3(11+x)

Question (6):
Assume that the number is x.
We want to get: four times the square of x increased by five times x
This means that:
i- We would square the x first
ii- multiply the result from step i by 4
iii- multiply 5 by x
iv- add the result from step ii to the result from step iii
The algebraic expression would be as follows:
4x^2 + 5x

Question (7):
Assume that the number is x.
We want to get: 23 more than the product of 7 and x
This means that we would multiply x by 7 and then add 23 to the product
The algebraic expression would be as follows:
7x+23

Hope this helps :)