Question

One half a number increased by three is greater than zero or less than or equal to negative three

Answer 1

let x be the name for that number, write the inequalities:

`0.5x+3>0 \\0.5x>-3\\x>-6\\\mbox{OR}\\0.5x+3\leq -3\\0.5x\leq -6\\x\leq -12\\`

This number x can be anything, except anything in the interval (-12, 6] (excluding -12, and including 6). Lmk if you have questions.

Answer 2

The solutions of given inequalities are
`x>-6` and
`x\leq -12` respectively.

Explanation:

It is given that one half a number increased by three is greater than zero or less than or equal to negative three.

Let x be the unknown number.

`(1)/(2)x+3>0` or
`(1)/(2)x+3\leq -3`

On solving first inequality,

`(1)/(2)x+3>0`

Subtract 3 from both sides.

`(1)/(2)x>-3`

Multiply both sides by 2.

`x>-6`

On solving second inequality,

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

Subtract 3 from both sides.

`(1)/(2)x\leq -6`

Multiply both sides by 2.

`x\leq -12`

Therefore, the solutions of given inequalities are
`x>-6` and
`x\leq -12` respectively.