1. Solve $17x + 12 = 54 - 4x$. Add $4x$ and subtract $12$: $$17x + 4x = 54 - 12$$ $$21x = 42$$ Divide both sides by $21$: $$x = \frac{42}{21} = 2$$ 2. Solve $6x - 16 = 15x - 9$. Subtract $6x$ and add $9$: $$-16 + 9 = 15x - 6x$$ $$-7 = 9x$$ Divide both sides by $9$: $$x = -\frac{7}{9}$$ 3. Solve $4x - 4 = 36 + 2x$. Subtract $2x$ and add $4$: $$4x - 2x = 36 + 4$$ $$2x = 40$$ Divide both sides by $2$: $$x = 20$$ 4. Solve $13x - 25 = 9x - 13$. Subtract $9x$ and add $25$: $$13x - 9x = -13 + 25$$ $$4x = 12$$ Divide both sides by $4$: $$x = 3$$ 5. Solve $9x + 2 = 7x + 15$. Subtract $7x$ and subtract $2$: $$9x - 7x = 15 - 2$$ $$2x = 13$$ Divide both sides by $2$: $$x = \frac{13}{2} = 6.5$$ 6. Solve $3x + 39 = 2x + 42$. Subtract $2x$ and subtract $39$: $$3x - 2x = 42 - 39$$ $$x = 3$$ 7. Solve $5x - 3x = 36 - 2x$. Simplify left side: $$2x = 36 - 2x$$ Add $2x$: $$2x + 2x = 36$$ $$4x = 36$$ Divide both sides by $4$: $$x = 9$$ 8. Solve $7x - 12 + 5 = 8x - 24$. Simplify left side: $$7x - 7 = 8x - 24$$ Subtract $7x$ and add $7$: $$-7 = x - 24$$ Add $24$: $$17 = x$$ 9. Solve $30 - x + 12 = 3x + 2$. Simplify left side: $$42 - x = 3x + 2$$ Add $x$ and subtract $2$: $$42 - 2 = 3x + x$$ $$40 = 4x$$ Divide both sides by $4$: $$x = 10$$ 10. Solve $6x - 30 = 60 - 8x - 20$. Simplify right side: $$6x - 30 = 40 - 8x$$ Add $8x$ and add $30$: $$6x + 8x = 40 + 30$$ $$14x = 70$$ Divide both sides by $14$: $$x = 5$$ 11. Solve $9x - 16 = 3x - (x - 5)$. Simplify right side: $$9x - 16 = 3x - x + 5 = 2x + 5$$ Subtract $2x$ and add $16$: $$9x - 2x = 5 + 16$$ $$7x = 21$$ Divide both sides by $7$: $$x = 3$$ 12. Solve $5x - 10 + 2x = 6(x + 1) - x$. Simplify both sides: $$7x - 10 = 6x + 6 - x$$ $$7x - 10 = 5x + 6$$ Subtract $5x$ and add $10$: $$7x - 5x = 6 + 10$$ $$2x = 16$$ Divide both sides by $2$: $$x = 8$$ 13. Solve $2(5x + 1) = x + 2$. Expand left side: $$10x + 2 = x + 2$$ Subtract $x$ and $2$: $$10x - x = 2 - 2$$ $$9x = 0$$ Divide both sides by $9$: $$x = 0$$ 14. Solve $5(x + 1) = 2(x - 5) + 6$. Expand: $$5x + 5 = 2x - 10 + 6$$ $$5x + 5 = 2x - 4$$ Subtract $2x$ and $5$: $$3x = -9$$ Divide both sides by $3$: $$x = -3$$ 15. Solve $3(x - 2) = 2(x - 3) - 5 = 0$. There seems to be a typo because two equal signs appear. Assuming the equation is $3(x - 2) = 2(x - 3) - 5$: Expand: $$3x - 6 = 2x - 6 - 5$$ $$3x - 6 = 2x - 11$$ Subtract $2x$ and add $6$: $$x = -5$$ 16. Solve $(3 - 2x) + 3(1 - 4x) - 4(1 - 5x) = 2(1 - 3x)$. Expand: $$3 - 2x + 3 - 12x - 4 + 20x = 2 - 6x$$ Combine like terms on left: $$(3 + 3 - 4) + (-2x - 12x + 20x) = 2 - 6x$$ $$2 + 6x = 2 - 6x$$ Subtract $2$: $$6x = -6x$$ Add $6x$: $$12x = 0$$ $$x = 0$$