simultaneous linear inequalities (i don't have money, im only in 7th grade, im sorry)
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
\[ \frac{m}{4} <x< \frac{6-m}{2} \text{or} x\in (\frac{m}{4}, \frac{6-m}{2}). \]
\[2x - 6 + m < 0 \Rightarrow 2x<6-m \Rightarrow x< \frac{6-m}{2}.\]
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
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