simultaneous linear inequalities (i don't have money, im only in 7th grade, im sorry)

2x - 6 + m < 0 
4x - m > 0

it asks to find the value of x. 

i really need help, my finals are tomorrow and it's almost midnight. i don't want to fail.

Linear Algebra Algebra
Sunny Sunny
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1 Answer

From the first equation we get 
\[2x - 6 + m < 0  \Rightarrow 2x<6-m \Rightarrow x< \frac{6-m}{2}.\]

From the second equation we get 
\[4x - m > 0 \Rightarrow 4x>m \Rightarrow x> \frac{m}{4}.\]

Putting these two together, we get 
\[ \frac{m}{4} <x< \frac{6-m}{2}      \text{or}     x\in (\frac{m}{4}, \frac{6-m}{2}). \]

Erdos Erdos
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