Solve for \( x \) : \( \begin{array}{l}\text { 2.1.1 } \quad p x+q x=a \\ 2.1 .2 \quad 2 x^{2}-5 x+2=0\end{array} \)

To solve the equations provided, let’s tackle each one separately. For the first equation \( px + qx = a \): Combine like terms: \[ (p + q)x = a \] Now, isolate \( x \): \[ x = \frac{a}{p + q} \] For the second equation \( 2x^2 - 5x + 2 = 0 \): We can use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 2 \), \( b = -5 \), and \( c = 2 \). First, calculate the discriminant: \[ b^2 - 4ac = (-5)^2 - 4 \cdot 2 \cdot 2 = 25 - 16 = 9 \] Now, substitute the values into the quadratic formula: \[ x = \frac{5 \pm \sqrt{9}}{2 \cdot 2} = \frac{5 \pm 3}{4} \] This gives us two solutions: \[ x = \frac{8}{4} = 2 \quad \text{and} \quad x = \frac{2}{4} = \frac{1}{2} \] Final solutions: 1. For \( px + qx = a \), \( x = \frac{a}{p + q} \) 2. For \( 2x^2 - 5x + 2 = 0 \), \( x = 2 \) and \( x = \frac{1}{2} \)