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Solve each of the following system of equations in R.

1. *x* + 3 > 0, 2*x* < 14

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#### Solution

\[x + 3 > 0\]

\[ \Rightarrow x > - 3\]

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

\[\text{ Also }, 2x < 14\]

\[ \Rightarrow x < 7 \left[ \text{ Dividing both the sides by 2 } \right]\]

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

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

\[\left( - 3, \infty \right) \cap \left( - \infty , 7 \right) = \left( - 3, 7 \right)\]

\[ \therefore x \in \left( - 3, 7 \right)\]

\[\text{ Thus, thesolution of the given set of inequalities is } \left( - 3, 7 \right) .\]

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