Question

2x + 6 ≥ 0, 4x − 7 < 0 

Answer 1

\[\text{ We have }, 2x + 6 \geq 0\]

\[ \Rightarrow 2x \geqslant - 6\]

\[ \Rightarrow x \geqslant - 3\]

\[ \Rightarrow x \in [ - 3, \infty ) . . . \left( i \right)\]

\[\text{ Also }, 4x - 7 < 0\]

\[ \Rightarrow 4x < 7\]

\[ \Rightarrow x < \frac{7}{4}\]

\[ \Rightarrow x \in \left( - \infty , \frac{7}{4} \right) . . . \left( ii \right)\]

\[\text{ Thus, the solution of the given inequations is the intersection of } \left( i \right) \text{ and } \left( ii \right) . \]

\[[ - 3, \infty ) \cap \left( - \infty \frac{7}{4} \right) = [ - 3, \frac{7}{4})\]

\[\text{ Thus, the solution of the given inequations is } [ - 3, \frac{7}{4}) .\]