Hello there!
Question:-
[tex] \tt \: 10 - 3x > - 23[/tex]
This is a inequality. We need to find the value of x of this inequality.
Solution:-
[tex]\sf \implies \: 10 - 3x > - 23[/tex]
This equation may be rewritten as ,
[tex]\sf \implies \: - 3x + 10 > - 23[/tex]
Firstly, Subtract both sides of this equation :-
[tex]\sf \implies \: - 3x+10 - 10> - 23 - 10[/tex]
On Simplification :-
As (+) and (-) equals to (+), So +10-10 will be represented as 10-10.It results to 0.
[tex]\sf \implies - 3x + 0 > - 23 - 10[/tex]
As (-) and (-) equals to (+), -23-10 will be represented as 23+10. But 23>10. 23 contains a minus (-) sign. The answer is -33.
[tex]\sf \implies - 3x > - 33[/tex]
Divide both sides by -3:-
[tex]\sf \implies \dfrac{ - 3x}{3} > \dfrac{33}{ 3} [/tex]
On Simplification:-
Cancel -3/-3, leave x, then cancel -33/3:-
[tex]\sf \implies \: \dfrac{3x}{3} > \dfrac{ - 33}{ - 3} [/tex]
[tex]\sf \implies \dfrac{ \cancel{ - 3}x}{ \cancel3} > \cancel\dfrac{ - 33}{-3} [/tex]
On cancelling -3/-3, 1x is the result, and on cancelling -33/-3, 11 is the result.
[tex]\sf \implies \: 1x < 11[/tex]
As we know,
[tex]\sf \implies \: \: 1x = x[/tex]
Then , 1x < 11 may be represented as :-
[tex]\sf \implies \: x < 11[/tex]
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Henceforth, the answer of the inequality is :-
[tex]\boxed{\huge \red {x < 11}}[/tex]
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I hope this helps!
Please let me know if you have any questions.
~MisterBrian
