1. **State the problem:** We want to solve simultaneous inequalities using MATLAB. 2. **Understanding simultaneous inequalities:** These are multiple inequalities that must be true at the same time. For example, solving $x > 2$ and $x < 5$ simultaneously means finding $x$ values that satisfy both. 3. **MATLAB approach:** MATLAB does not have a direct function for inequalities like equations, but we can use logical operators and functions like `solve` for symbolic inequalities. 4. **Example problem:** Solve the system $x + y > 3$ and $x - y < 1$. 5. **Step-by-step in MATLAB:** - Define symbolic variables: `syms x y` - Write inequalities: `ineq1 = x + y > 3; ineq2 = x - y < 1;` - Use `solve` with inequalities: `S = solve([ineq1, ineq2], [x, y], 'ReturnConditions', true);` 6. **Explanation:** `solve` returns conditions on $x$ and $y$ that satisfy both inequalities simultaneously. 7. **Interpreting results:** The output gives the solution set or conditions describing all $(x,y)$ pairs that satisfy the inequalities. 8. **Summary:** To solve simultaneous inequalities in MATLAB, define symbolic variables, express inequalities, and use `solve` with the `'ReturnConditions'` option to get the solution set. This method works well for linear inequalities and can be extended to more variables and inequalities.