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:-

$\sf \longmapsto \: \dfrac{17x}{17} > \dfrac{0}{17}$

On Simplification:-

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

$\sf \longmapsto \dfrac{ \cancel{17}x}{ \cancel{17}} > \dfrac{0}{17}$

$\sf \longmapsto \: x > 0$

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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