1. **State the problem:** We need to find the solution for each linear equation and match it to one of the numbers: -3, -2, 3, or 7. 2. **Equation 1:** $$\frac{1}{4} x + \frac{5}{3} x - 4 = 2 - \frac{1}{12} x$$ Combine like terms on the left: $$\frac{1}{4} x + \frac{5}{3} x = \frac{3}{12} x + \frac{20}{12} x = \frac{23}{12} x$$ Rewrite equation: $$\frac{23}{12} x - 4 = 2 - \frac{1}{12} x$$ Add $\frac{1}{12} x$ to both sides: $$\frac{23}{12} x + \frac{1}{12} x - 4 = 2$$ $$\frac{24}{12} x - 4 = 2$$ Simplify fraction: $$2 x - 4 = 2$$ Add 4 to both sides: $$2 x = 6$$ Divide both sides by 2: $$x = \frac{6}{2}$$ $$x = 3$$ 3. **Equation 2:** $$3.2 b - 4.7 = 3 b - 3.3$$ Subtract $3 b$ from both sides: $$3.2 b - 3 b - 4.7 = -3.3$$ $$0.2 b - 4.7 = -3.3$$ Add 4.7 to both sides: $$0.2 b = 1.4$$ Divide both sides by 0.2: $$b = \frac{1.4}{0.2}$$ $$b = 7$$ 4. **Equation 3:** $$4.6 y - y + 4 = y - 1.2$$ Combine like terms on the left: $$3.6 y + 4 = y - 1.2$$ Subtract $y$ from both sides: $$3.6 y - y + 4 = -1.2$$ $$2.6 y + 4 = -1.2$$ Subtract 4 from both sides: $$2.6 y = -5.2$$ Divide both sides by 2.6: $$y = \frac{-5.2}{2.6}$$ $$y = -2$$ 5. **Equation 4:** $$7.5 c - 2.5 c + 8 = -7$$ Combine like terms on the left: $$5 c + 8 = -7$$ Subtract 8 from both sides: $$5 c = -15$$ Divide both sides by 5: $$c = \frac{-15}{5}$$ $$c = -3$$ **Final matches:** - Equation 1 solution: 3 - Equation 2 solution: 7 - Equation 3 solution: -2 - Equation 4 solution: -3