1. The problem is to solve a system of 2 simultaneous inequalities. 2. A system of inequalities involves finding the set of values that satisfy both inequalities at the same time. 3. The general approach is to solve each inequality separately and then find the intersection of their solution sets. 4. For example, consider the system: $$\begin{cases} 2x + 3 > 7 \\ x - 4 \leq 1 \end{cases}$$ 5. Solve the first inequality: $$2x + 3 > 7$$ Subtract 3 from both sides: $$2x > 4$$ Divide both sides by 2: $$x > 2$$ 6. Solve the second inequality: $$x - 4 \leq 1$$ Add 4 to both sides: $$x \leq 5$$ 7. The solution to the system is the intersection of the two solution sets: $$x > 2 \quad \text{and} \quad x \leq 5$$ 8. Therefore, the solution is: $$2 < x \leq 5$$ This means all values of $x$ greater than 2 and less than or equal to 5 satisfy both inequalities.