1. **Stating the problem:** We are given several algebraic expressions and equations to build up and undo, and to solve for variables. 2. **Building and undoing expressions:** - Expression 1: $3x - 2$ - Build: Start with $x$, multiply by 3, then subtract 2. - Undo: Start with the expression, add 2, then divide by 3. - Expression 2: $\frac{x}{6} + 5$ - Build: Start with $x$, divide by 6, then add 5. - Undo: Start with the expression, subtract 5, then multiply by 6. - Expression 3: $-4(x + 3)$ - Build: Start with $x$, add 3, then multiply by -4. - Undo: Start with the expression, divide by -4, then subtract 3. - Expression 4: $\frac{x + 3}{-2}$ - Build: Start with $x$, add 3, then divide by -2. - Undo: Start with the expression, multiply by -2, then subtract 3. 3. **Solving equations:** - Equation 1: $x - 7 = 3$ - Add 7 to both sides: $$x - 7 + 7 = 3 + 7$$ $$x = 10$$ - Equation 2: $\frac{b}{2} = 16$ - Multiply both sides by 2: $$\cancel{\frac{b}{2}} \times 2 = 16 \times 2$$ $$b = 32$$ - Equation 3: $4x + 2 = 18$ - Subtract 2 from both sides: $$4x + 2 - 2 = 18 - 2$$ $$4x = 16$$ - Divide both sides by 4: $$\cancel{4x} \div \cancel{4} = 16 \div 4$$ $$x = 4$$ - Equation 4: $-3(d - 6) = 21$ - Divide both sides by -3: $$\cancel{-3}(d - 6) \div \cancel{-3} = 21 \div -3$$ $$d - 6 = -7$$ - Add 6 to both sides: $$d - 6 + 6 = -7 + 6$$ $$d = -1$$ 4. **Summary:** We have shown how to build and undo each expression step-by-step and solved each equation with clear intermediate steps and explanations.