1. **Problem statement:** Solve the equation $2(3x + 2) = 2x + 28$. 2. **Distribute:** Apply the distributive property to the left side: $$2 \times 3x + 2 \times 2 = 6x + 4$$ So the equation becomes: $$6x + 4 = 2x + 28$$ 3. **Bring variables to one side:** Subtract $2x$ from both sides: $$6x + 4 - \cancel{2x} = \cancel{2x} + 28 - 2x$$ $$6x - 2x + 4 = 28$$ $$4x + 4 = 28$$ 4. **Isolate variable term:** Subtract 4 from both sides: $$4x + 4 - 4 = 28 - 4$$ $$4x = 24$$ 5. **Solve for $x$:** Divide both sides by 4: $$\frac{4x}{\cancel{4}} = \frac{24}{\cancel{4}}$$ $$x = 6$$ --- 1. **Problem statement:** Solve the equation $5y + 13 = -43 - 3y$. 2. **Bring variables to one side:** Add $3y$ to both sides: $$5y + 13 + 3y = -43 - 3y + 3y$$ $$8y + 13 = -43$$ 3. **Isolate variable term:** Subtract 13 from both sides: $$8y + 13 - 13 = -43 - 13$$ $$8y = -56$$ 4. **Solve for $y$:** Divide both sides by 8: $$\frac{8y}{\cancel{8}} = \frac{-56}{\cancel{8}}$$ $$y = -7$$ --- 1. **Problem statement:** Solve the equation $4(2a + 2) = 8(2 - 3a)$. 2. **Distribute:** Left side: $$4 \times 2a + 4 \times 2 = 8a + 8$$ Right side: $$8 \times 2 - 8 \times 3a = 16 - 24a$$ Equation becomes: $$8a + 8 = 16 - 24a$$ 3. **Bring variables to one side:** Add $24a$ to both sides: $$8a + 24a + 8 = 16 - 24a + 24a$$ $$32a + 8 = 16$$ 4. **Isolate variable term:** Subtract 8 from both sides: $$32a + 8 - 8 = 16 - 8$$ $$32a = 8$$ 5. **Solve for $a$:** Divide both sides by 32: $$\frac{32a}{\cancel{32}} = \frac{8}{\cancel{32}}$$ $$a = \frac{1}{4}$$