1. **State the problem:** We need to find the solutions for each equation and then arrange the equations in increasing order of their solution values. 2. **Equation 1:** $$\frac{1}{4}x + \frac{5}{2}x - 2 = 4 - \frac{1}{4}x$$ Combine like terms on the left: $$\frac{1}{4}x + \frac{5}{2}x = \frac{1}{4}x + \frac{10}{4}x = \frac{11}{4}x$$ Rewrite the equation: $$\frac{11}{4}x - 2 = 4 - \frac{1}{4}x$$ Add $\frac{1}{4}x$ to both sides: $$\frac{11}{4}x + \frac{1}{4}x - 2 = 4$$ $$\frac{12}{4}x - 2 = 4$$ Simplify: $$3x - 2 = 4$$ Add 2 to both sides: $$3x = 6$$ Divide both sides by 3: $$x = \frac{6}{3}$$ $$x = 2$$ 3. **Equation 2:** $$7.9x + x + 4 = -1.1x - 16$$ Combine like terms on the left: $$8.9x + 4 = -1.1x - 16$$ Add $1.1x$ to both sides: $$8.9x + 1.1x + 4 = -16$$ $$10x + 4 = -16$$ Subtract 4 from both sides: $$10x = -20$$ Divide both sides by 10: $$x = \frac{-20}{10}$$ $$x = -2$$ 4. **Equation 3:** $$3.2x + 5.7 = -2.5x$$ Add $2.5x$ to both sides: $$3.2x + 2.5x + 5.7 = 0$$ $$5.7x + 5.7 = 0$$ Subtract 5.7 from both sides: $$5.7x = -5.7$$ Divide both sides by 5.7: $$x = \frac{-5.7}{5.7}$$ $$x = -1$$ 5. **Equation 4:** $$10.1x - 1.6x + 44 = -7$$ Combine like terms on the left: $$8.5x + 44 = -7$$ Subtract 44 from both sides: $$8.5x = -51$$ Divide both sides by 8.5: $$x = \frac{-51}{8.5}$$ Calculate: $$x = -6$$ 6. **Arrange in increasing order:** Solutions are: Equation 4: $-6$ Equation 2: $-2$ Equation 3: $-1$ Equation 1: $2$ So the order from smallest to largest solution is: Equation 4, Equation 2, Equation 3, Equation 1.