Question

Write the expressions "Four times the difference of a number and 7 is 32", "One third of a number is 12 less than the number itself", "Ten increased by the quotient of a number and 2 is -15", and "One less than the product of a number and 3 is 5 more than the number itself".

Answer 1

Part 1) "Four times the difference of a number and
`7` is
`32`"

Let

x--------> the number

we know that

the expressions is equal to

`4(x-7)=32`

therefore

the answer part 1) is

`4(x-7)=32`

Part 2) "One third of a number is
`12` less than the number itself"

Let

x--------> the number

we know that

the expressions is equal to

`(1)/(3) x=(x-12 )`

therefore

the answer part 2) is

`(1)/(3) x=(x-12 )`

Part 3) "Ten increased by the quotient of a number and
`2` is
`-15`"

Let

x---------> the number

we know that

the expressions is equal to

`10+ ((x)/(2) )= -15`

therefore

the answer Part 3) is

`10+ ((x)/(2) )= -15`

Part 4) "One less than the product of a number and
`3` is
`5` more than the number itself"

Let

x---------> the number

we know that

the expressions is equal to

`(3x)-1=5+x`

therefore

the answer Part 4) is

`(3x)-1=5+x`