Hello BATAPAAKO!
[tex] \huge \boxed{\mathbb{QUESTION} \downarrow}[/tex]
Solve the inequality: x+10>2x/5.
[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
[tex]x + 10 \gt \frac { 2 x } { 5 } \\ [/tex]
Firstly, multiply both sides of the equation by 5.
[tex]5(x + 10) > 2x \\ = 5x + 50 > 2x[/tex]
Since 5 is greater than 0, the direction of the inequality will remain unchanged. Now, subtract 2x from both the sides.
[tex]5x + 50 > 20 \\ = 5x + 50 - 2x > 0[/tex]
Combine 5x & -2x to get 3x.
[tex]5x + 50 - 2x > 0 \\ = 5x - 2x + 50 > 0 \\ = 3x + 50 > 0[/tex]
Now, subtract 50 from both the sides. Remember :- anything subtracted by 0 will result in its negation. So 50 subtracted from 0 will give you -50.
[tex]3x + 50 > 0 \\ = 3x > - 50[/tex]
Divide both sides of the equation by 3. Again, since 3 is > 0, the direction of inequality will remain unchanged.
[tex]3x > - 50 \\ = \large\boxed{\boxed{ \bf \: x > - \frac{ 50}{3} }}[/tex]
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Hope it'll help you!
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