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

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remotecontrolbrain remotecontrolbrain · Answer 1 · 2018-10-10T20:20:21+02:00

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

[tex]0.5x+3>0 \\0.5x>-3\\x>-6\\\mbox{OR}\\0.5x+3\leq -3\\0.5x\leq -6\\x\leq -12\\[/tex]

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

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erinna erinna · Answer 2 · 2019-09-18T13:56:34+02:00

Answer:

The solutions of given inequalities are [tex]x>-6[/tex] and [tex]x\leq -12[/tex] respectively.

Step-by-step 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.

[tex]\frac{1}{2}x+3>0[/tex] or [tex]\frac{1}{2}x+3\leq -3[/tex]

On solving first inequality,

[tex]\frac{1}{2}x+3>0[/tex]

Subtract 3 from both sides.

[tex]\frac{1}{2}x>-3[/tex]

Multiply both sides by 2.

[tex]x>-6[/tex]

On solving second inequality,

[tex]\frac{1}{2}x+3\leq -3[/tex]

Subtract 3 from both sides.

[tex]\frac{1}{2}x\leq -6[/tex]

Multiply both sides by 2.

[tex]x\leq -12[/tex]

Therefore, the solutions of given inequalities are [tex]x>-6[/tex] and [tex]x\leq -12[/tex] respectively.