Question

find all numbers such that a third of a number increased by half that number is at least 3 less than that same number

Answer 1

All real numbers less than or equal to 18

Explanation:

Let

x -----> the number

we know that

The algebraic expression that represent this situation is

`(1)/(3)x+(1)/(2)x \geq x-3`

Solve for x

Multiply by 6 both sides to remove the fractions

`2x+3x \geq6x-18`

Combine like terms left side

`5x \geq6x-18`

Adds 18 both sides

`5x+18 \geq 6x`

Subtract 5x both sides

`18 \geq 6x-5x`

`18 \geq x`

Rewrite

`x\leq 18`

All real numbers less than or equal to 18