Step-by-step explanation:
We are to get the expression for the following statements;
1) The difference of nine times a number x and the quotient of that number and 5.
The product of nine and a number x is expressed as;
[tex]=9 \times x\\= 9x[/tex]
The quotient of that number and 5.
[tex]= \frac{x}{5}[/tex]
The difference between both expression;
[tex]9x - \frac{x}{5}[/tex]
Hence, the difference of nine times a number x and the quotient of that number and 5 is expressed as [tex]9x - \frac{x}{5}[/tex]
2) Eight more than the quotient of twelve and a number n
Quotient of twelve and a number n is expressed as:
[tex]\frac{n}{12}[/tex]
Eight more than the resulting function is;
[tex]\frac{n}{12}+8[/tex]
Hence eight more than the quotient of twelve and a number n is expressed as [tex]\frac{n}{12}+8[/tex]
3) The product of a number and the quantity 'six minus the number' plus the quotient of eight and the number.
Let the number be x:
six minus the number is expressed as;
[tex]6-x[/tex]
product of a number x and the quantity 'six minus the number is;
[tex]x(6-x)[/tex]
quotient of eight and the number is;
[tex]\frac{8}{x}[/tex]
Taking the resulting sum of the last two expression
[tex]x(6-x) + 8x[/tex]
Hence the product of a number and the quantity 'six minus the number' plus the quotient of eight and the number is expressed as;
[tex]x(6-x) + 8x[/tex]
4) Sum of three consecutive even integers. 2x + (2x + 2) + (2x + 4).
Let the first even number be 2x
The consecutive even numbers are gotten by adding 2 to the preceding number. The two consecutive even integers are 2x+2 and 2x+2+2
the sum of three consecutive even integers is expressed as;
[tex]= 2x +(2x+2)+(2x+2+2)\\= 2x+(2x+2)+(2x+4)[/tex]
