Question

Two thirds of a number decreased by 27 is at least 9

Answer 1

The mathematical statement can be written as follows

`(2)/(3)x-27\geq9`

which has solution as

⇒
`x\geq54`

Explanation:

Given:

Two thirds of a number decreased by 27 is at least 9.

This statement can be transformed into a mathematical statement.

Taking the unknown number as
`x` and putting the inequality
`\geq9` as the result is at least 9.

So, we have

`(2)/(3)x-27\geq9`

Adding 27 both sides

`(2)/(3)x-27+27\geq 9+27`

`(2)/(3)x\geq 36`

Multiplying both sides by 3.

`3*(2)/(3)x\geq 36* 3`

`2x\geq108`

Dividing both sides by 2.

`(2x)/(2)\geq(108)/(2)`

∴
`x\geq54`