Algebra 1 Worksheets with Answers PDF | Printable Algebra 1 Math ... - Free Printable

Here are the solutions for all the linear equations in the worksheet.

Section A

These equations follow the form $ax + b = c$. To solve them, you first subtract $b$ from both sides, then divide by $a$.

1) $7x + 9 = 23$
* Subtract 9: $7x = 14$
* Divide by 7: $x = 2$

2) $5x + 7 = 42$
* Subtract 7: $5x = 35$
* Divide by 5: $x = 7$

3) $4x + 3 = 51$
* Subtract 3: $4x = 48$
* Divide by 4: $x = 12$

4) $9x + 5 = 41$
* Subtract 5: $9x = 36$
* Divide by 9: $x = 4$

5) $4x + 2 = 34$
* Subtract 2: $4x = 32$
* Divide by 4: $x = 8$

6) $11x + 3 = 36$
* Subtract 3: $11x = 33$
* Divide by 11: $x = 3$

7) $10x + 2 = 72$
* Subtract 2: $10x = 70$
* Divide by 10: $x = 7$

8) $7x + 3 = 52$
* Subtract 3: $7x = 49$
* Divide by 7: $x = 7$

9) $6x + 5 = 17$
* Subtract 5: $6x = 12$
* Divide by 6: $x = 2$

10) $4x + 7 = 9$
* Subtract 7: $4x = 2$
* Divide by 4: $x = 0.5$ (or $\frac{1}{2}$)

11) $8x + 11 = 15$
* Subtract 11: $8x = 4$
* Divide by 8: $x = 0.5$ (or $\frac{1}{2}$)

12) $4x + 17 = 18$
* Subtract 17: $4x = 1$
* Divide by 4: $x = 0.25$ (or $\frac{1}{4}$)

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Section B

These equations have the constant term first (e.g., $b + ax = c$). The steps are the same: subtract the constant, then divide.

1) $1 + 6x = 19$
* Subtract 1: $6x = 18$
* Divide by 6: $x = 3$

2) $9 + 7x = 30$
* Subtract 9: $7x = 21$
* Divide by 7: $x = 3$

3) $3 + 2x = 17$
* Subtract 3: $2x = 14$
* Divide by 2: $x = 7$

4) $11 + 5x = 71$
* Subtract 11: $5x = 60$
* Divide by 5: $x = 12$

5) $5 + 3x = 32$
* Subtract 5: $3x = 27$
* Divide by 3: $x = 9$

6) $4 + 5x = 44$
* Subtract 4: $5x = 40$
* Divide by 5: $x = 8$

7) $23 = x + 8$
* Subtract 8: $15 = x$
* $x = 15$

8) $28 = 3x + 1$
* Subtract 1: $27 = 3x$
* Divide by 3: $x = 9$

9) $53 = 8x + 5$
* Subtract 5: $48 = 8x$
* Divide by 8: $x = 6$

10) $13 = 11 + 4x$
* Subtract 11: $2 = 4x$
* Divide by 4: $x = 0.5$ (or $\frac{1}{2}$)

11) $7 = 8x + 3$
* Subtract 3: $4 = 8x$
* Divide by 8: $x = 0.5$ (or $\frac{1}{2}$)

12) $12 = 7 + 15x$
* Subtract 7: $5 = 15x$
* Divide by 15: $x = \frac{1}{3}$

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Section C

These equations involve subtraction (e.g., $ax - b = c$). To solve, you add $b$ to both sides first, then divide.

1) $4x - 1 = 31$
* Add 1: $4x = 32$
* Divide by 4: $x = 8$

2) $3x - 4 = 29$
* Add 4: $3x = 33$
* Divide by 3: $x = 11$

3) $6x - 5 = 31$
* Add 5: $6x = 36$
* Divide by 6: $x = 6$

4) $8x - 2 = 46$
* Add 2: $8x = 48$
* Divide by 8: $x = 6$

5) $2x - 7 = 21$
* Add 7: $2x = 28$
* Divide by 2: $x = 14$

6) $7x - 3 = 18$
* Add 3: $7x = 21$
* Divide by 7: $x = 3$

7) $9x - 4 = 32$
* Add 4: $9x = 36$
* Divide by 9: $x = 4$

8) $5x - 1 = 64$
* Add 1: $5x = 65$
* Divide by 5: $x = 13$

9) $12x - 9 = 39$
* Add 9: $12x = 48$
* Divide by 12: $x = 4$

10) $2x - 1 = 2$
* Add 1: $2x = 3$
* Divide by 2: $x = 1.5$ (or $\frac{3}{2}$)

11) $4x - 8 = 10$
* Add 8: $4x = 18$
* Divide by 4: $x = 4.5$ (or $\frac{9}{2}$)

12) $15x - 2 = 3$
* Add 2: $15x = 5$
* Divide by 15: $x = \frac{1}{3}$

Final Answer:
Section A: 1) 2, 2) 7, 3) 12, 4) 4, 5) 8, 6) 3, 7) 7, 8) 7, 9) 2, 10) 0.5, 11) 0.5, 12) 0.25
Section B: 1) 3, 2) 3, 3) 7, 4) 12, 5) 9, 6) 8, 7) 15, 8) 9, 9) 6, 10) 0.5, 11) 0.5, 12) 1/3
Section C: 1) 8, 2) 11, 3) 6, 4) 6, 5) 14, 6) 3, 7) 4, 8) 13, 9) 4, 10) 1.5, 11) 4.5, 12) 1/3