Question

Which inequality is the solution to 7 x + 13 + 2 ( 5 x − 3 ) > 7 ?

Answer 1

Question:-

`7 x + 13 + 2 ( 5 x − 3 ) > 7`

We need to solve this inequality.

Solution:-

`\sf \longmapsto7 x + 13 + 2 ( 5 x − 3 ) > 7`

Firstly, simplify the two sides of the inequality :-

On Simplification:-

`\sf \longmapsto \: 17x+7>7`

This is our new equation.

Then, Subtract 7 from both sides :-

`\sf \longmapsto17x+7 - 7>7 - 7`

On Simplification:-

As (-) and (+) = (-),It will be 7-7.

`\sf \longmapsto17x + 0 > 0`

`\sf \longmapsto \: 17x > 0`

Divide the two sides by 17:-

`\sf \longmapsto \: (17x)/(17) > (0)/(17)`

On Simplification:-

Cancel 17 and 17, leave x.If the numerator or denominator is 0, then the solution of that Fraction is 0.

`\sf \longmapsto \frac{ \cancel{17}x}{ \cancel{17}} > (0)/(17)`

`\sf \longmapsto \: x > 0`

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Henceforth the answer of the inequality is :-

`\huge{\boxed{\boxed{\bf x > 0}}}`

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I hope this helps!

Please let me know if you have any questions.

~MisterBrian