Set of 16 linear equations for solving algebraic expressions.

Here are the step-by-step solutions for each equation. The goal is to get $x$ by itself on one side of the equal sign.

(1) $17x + 12 = 54 - 4x$
* Add $4x$ to both sides: $21x + 12 = 54$
* Subtract 12 from both sides: $21x = 42$
* Divide by 21: $x = 2$

(2) $6x - 16 = 5x - 9$
* Subtract $5x$ from both sides: $x - 16 = -9$
* Add 16 to both sides: $x = 7$

(3) $4x - 4 = 3x + 2$
* Subtract $3x$ from both sides: $x - 4 = 2$
* Add 4 to both sides: $x = 6$

(4) $13x - 25 = 9x - 13$
* Subtract $9x$ from both sides: $4x - 25 = -13$
* Add 25 to both sides: $4x = 12$
* Divide by 4: $x = 3$

(5) $9x + 2 = 7x + 15$
* Subtract $7x$ from both sides: $2x + 2 = 15$
* Subtract 2 from both sides: $2x = 13$
* Divide by 2: $x = 6.5$ (or $\frac{13}{2}$)

(6) $3x + 39 = 2x + 42$
* Subtract $2x$ from both sides: $x + 39 = 42$
* Subtract 39 from both sides: $x = 3$

(7) $5x - 3x = 36 - x$
* Simplify the left side ($5x - 3x$): $2x = 36 - x$
* Add $x$ to both sides: $3x = 36$
* Divide by 3: $x = 12$

(8) $7x - 12 + 5 = 8x - 24$
* Simplify the left side ($-12 + 5$): $7x - 7 = 8x - 24$
* Subtract $7x$ from both sides: $-7 = x - 24$
* Add 24 to both sides: $17 = x$

(9) $30 - x + 12 = 3x + 2$
* Simplify the left side ($30 + 12$): $42 - x = 3x + 2$
* Add $x$ to both sides: $42 = 4x + 2$
* Subtract 2 from both sides: $40 = 4x$
* Divide by 4: $x = 10$

(10) $6x - 30 = 60 - 8x - 20$
* Simplify the right side ($60 - 20$): $6x - 30 = 40 - 8x$
* Add $8x$ to both sides: $14x - 30 = 40$
* Add 30 to both sides: $14x = 70$
* Divide by 14: $x = 5$

(11) $9x - 16 = 3x - (x - 5)$
* Distribute the negative sign on the right side: $9x - 16 = 3x - x + 5$
* Simplify the right side: $9x - 16 = 2x + 5$
* Subtract $2x$ from both sides: $7x - 16 = 5$
* Add 16 to both sides: $7x = 21$
* Divide by 7: $x = 3$

(12) $5x - 10 + 2x = 6(x + 1) - x$
* Simplify the left side: $7x - 10 = 6(x + 1) - x$
* Distribute the 6 on the right side: $7x - 10 = 6x + 6 - x$
* Simplify the right side: $7x - 10 = 5x + 6$
* Subtract $5x$ from both sides: $2x - 10 = 6$
* Add 10 to both sides: $2x = 16$
* Divide by 2: $x = 8$

(13) $2(5x + 1) = x + 2$
* Distribute the 2 on the left side: $10x + 2 = x + 2$
* Subtract $x$ from both sides: $9x + 2 = 2$
* Subtract 2 from both sides: $9x = 0$
* Divide by 9: $x = 0$

(14) $5(x + 1) = 2(x - 5) + 6$
* Distribute on both sides: $5x + 5 = 2x - 10 + 6$
* Simplify the right side: $5x + 5 = 2x - 4$
* Subtract $2x$ from both sides: $3x + 5 = -4$
* Subtract 5 from both sides: $3x = -9$
* Divide by 3: $x = -3$

(15) $3(x - 2) - 2(x - 3) - 5 = 0$
* Distribute: $3x - 6 - 2x + 6 - 5 = 0$
*(Note: $-2 \times -3$ becomes positive 6)*
* Combine like terms ($3x - 2x$ and $-6 + 6 - 5$): $x - 5 = 0$
* Add 5 to both sides: $x = 5$

(16) $(3 - 2x) + 3(1 - 4x) - 4(1 - 5x) = 2(1 - 3x)$
* Distribute: $3 - 2x + 3 - 12x - 4 + 20x = 2 - 6x$
* Combine like terms on the left side:
* $x$ terms: $-2x - 12x + 20x = 6x$
* Numbers: $3 + 3 - 4 = 2$
* Equation becomes: $6x + 2 = 2 - 6x$
* Add $6x$ to both sides: $12x + 2 = 2$
* Subtract 2 from both sides: $12x = 0$
* Divide by 12: $x = 0$

Final Answer:
(1) x = 2
(2) x = 7
(3) x = 6
(4) x = 3
(5) x = 6.5
(6) x = 3
(7) x = 12
(8) x = 17
(9) x = 10
(10) x = 5
(11) x = 3
(12) x = 8
(13) x = 0
(14) x = -3
(15) x = 5
(16) x = 0