Algebra Equations | Worksheet - Free Printable

Here are the step-by-step solutions for the algebra equations on the worksheet.

Part 1: Solve for X

1.) $4x + 16 = 24$
* Subtract 16 from both sides: $4x = 8$
* Divide by 4: $x = 2$

2.) $33 - 3x = 12$
* Subtract 33 from both sides: $-3x = -21$
* Divide by -3: $x = 7$

3.) $x - 6 = 17$
* Add 6 to both sides: $x = 23$

4.) $10x - 6 = 34$
* Add 6 to both sides: $10x = 40$
* Divide by 10: $x = 4$

5.) $23 + 6x = 29$
* Subtract 23 from both sides: $6x = 6$
* Divide by 6: $x = 1$

6.) $2x + 8 = 16$
* Subtract 8 from both sides: $2x = 8$
* Divide by 2: $x = 4$

7.) $4(x + 3) - 2x + 8 = 28$
* Distribute the 4: $4x + 12 - 2x + 8 = 28$
* Combine like terms ($4x - 2x$ and $12 + 8$): $2x + 20 = 28$
* Subtract 20 from both sides: $2x = 8$
* Divide by 2: $x = 4$

8.) $34 - 5x + 2(x - 2) = 15$
* Distribute the 2: $34 - 5x + 2x - 4 = 15$
* Combine like terms ($-5x + 2x$ and $34 - 4$): $-3x + 30 = 15$
* Subtract 30 from both sides: $-3x = -15$
* Divide by -3: $x = 5$

9.) $9x - 6(x + 2) - 6 = 12$
* Distribute the -6: $9x - 6x - 12 - 6 = 12$
* Combine like terms ($9x - 6x$ and $-12 - 6$): $3x - 18 = 12$
* Add 18 to both sides: $3x = 30$
* Divide by 3: $x = 10$

10.) $10 + 3x + 2(x - 3) = 29$
* Distribute the 2: $10 + 3x + 2x - 6 = 29$
* Combine like terms ($3x + 2x$ and $10 - 6$): $5x + 4 = 29$
* Subtract 4 from both sides: $5x = 25$
* Divide by 5: $x = 5$

---

Part 2: Solve for X, where Y equals the number given

1.) $y = 4$, equation: $7x - 3 + 4y = 27$
* Substitute 4 for y: $7x - 3 + 4(4) = 27$
* Multiply: $7x - 3 + 16 = 27$
* Combine numbers: $7x + 13 = 27$
* Subtract 13 from both sides: $7x = 14$
* Divide by 7: $x = 2$

2.) $y = 2$, equation: $2y + 8 + 5x = 27$
* Substitute 2 for y: $2(2) + 8 + 5x = 27$
* Multiply: $4 + 8 + 5x = 27$
* Combine numbers: $12 + 5x = 27$
* Subtract 12 from both sides: $5x = 15$
* Divide by 5: $x = 3$

3.) $y = 5$, equation: $4(x - 3) + y = 21$
* Substitute 5 for y: $4(x - 3) + 5 = 21$
* Subtract 5 from both sides: $4(x - 3) = 16$
* Divide both sides by 4: $x - 3 = 4$
* Add 3 to both sides: $x = 7$

4.) $y = 3$, equation: $4y + 6(5 - 2x) = 6$
* Substitute 3 for y: $4(3) + 6(5 - 2x) = 6$
* Multiply: $12 + 6(5 - 2x) = 6$
* Subtract 12 from both sides: $6(5 - 2x) = -6$
* Divide both sides by 6: $5 - 2x = -1$
* Subtract 5 from both sides: $-2x = -6$
* Divide by -2: $x = 3$

Final Answer:
Part 1:
1) x = 2
2) x = 7
3) x = 23
4) x = 4
5) x = 1
6) x = 4
7) x = 4
8) x = 5
9) x = 10
10) x = 5

Part 2:
1) x = 2
2) x = 3
3) x = 7
4) x = 3