\( \left. \begin{array} { l l } { 1.1 .3 } & { 2 x ^ { 2 } - 5 x + 3 < 0 } \\ { 1.1 .4 } & { 2 \sqrt { x + 2 } = x - 1 } \end{array} \right. \)

To solve the quadratic inequality \(2x^2 - 5x + 3 < 0\), you first need to find the roots of the corresponding equation \(2x^2 - 5x + 3 = 0\) using the quadratic formula. The roots split the number line into intervals that can be tested to find where the inequality holds. The roots are approximately \(x = 1\) and \(x = 1.5\); thus, check the intervals \((-∞, 1)\), \((1, 1.5)\), and \((1.5, +∞)\) to determine where the quadratic is negative. For \(2\sqrt{x+2} = x - 1\), it's helpful to isolate the radical. Begin by squaring both sides to eliminate the square root, yielding \(4(x + 2) = (x - 1)^2\). Expanding and rearranging gives a quadratic equation which can then be solved for \(x\). Remember to check for extraneous solutions, especially since squaring can introduce more roots than the original equation.