solving-basic-algebraic-equationsAlgebra & Functions Worksheets ... - Free Printable

Here are the step-by-step solutions for each equation on the worksheet.

Part 1: Solve for X

1.) $18 + 2x = 24$
* Subtract 18 from both sides: $2x = 6$
* Divide by 2: $x = 3$

2.) $4x - 3 = 21$
* Add 3 to both sides: $4x = 24$
* Divide by 4: $x = 6$

3.) $2x + 10 = 20$
* Subtract 10 from both sides: $2x = 10$
* Divide by 2: $x = 5$

4.) $8x - 6 = 18$
* Add 6 to both sides: $8x = 24$
* Divide by 8: $x = 3$

5.) $12 + 3x = 27$
* Subtract 12 from both sides: $3x = 15$
* Divide by 3: $x = 5$

6.) $5x - 7 = 18$
* Add 7 to both sides: $5x = 25$
* Divide by 5: $x = 5$

7.) $3(x - 3) - x - 2 = 17$
* Distribute the 3 into the parentheses: $3x - 9 - x - 2 = 17$
* Combine like terms ($3x - x$ and $-9 - 2$): $2x - 11 = 17$
* Add 11 to both sides: $2x = 28$
* Divide by 2: $x = 14$

8.) $22 - 2x + 4(x - 2) = 34$
* Distribute the 4 into the parentheses: $22 - 2x + 4x - 8 = 34$
* Combine like terms ($-2x + 4x$ and $22 - 8$): $2x + 14 = 34$
* Subtract 14 from both sides: $2x = 20$
* Divide by 2: $x = 10$

9.) $7x - 4(x + 4) + 20 = 25$
* Distribute the -4 into the parentheses: $7x - 4x - 16 + 20 = 25$
* Combine like terms ($7x - 4x$ and $-16 + 20$): $3x + 4 = 25$
* Subtract 4 from both sides: $3x = 21$
* Divide by 3: $x = 7$

10.) $11 + 5x + 2(x - 5) = 8$
* Distribute the 2 into the parentheses: $11 + 5x + 2x - 10 = 8$
* Combine like terms ($5x + 2x$ and $11 - 10$): $7x + 1 = 8$
* Subtract 1 from both sides: $7x = 7$
* Divide by 7: $x = 1$

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

1.) $y = 6$, $x = ?$
Equation: $7x - 2 + 4y = 36$
* Substitute 6 for y: $7x - 2 + 4(6) = 36$
* Multiply: $7x - 2 + 24 = 36$
* Combine numbers: $7x + 22 = 36$
* Subtract 22 from both sides: $7x = 14$
* Divide by 7: $x = 2$

2.) $y = 3$, $x = ?$
Equation: $2y + 8 + 5x = 29$
* Substitute 3 for y: $2(3) + 8 + 5x = 29$
* Multiply: $6 + 8 + 5x = 29$
* Combine numbers: $14 + 5x = 29$
* Subtract 14 from both sides: $5x = 15$
* Divide by 5: $x = 3$

Final Answer:
1) x = 3
2) x = 6
3) x = 5
4) x = 3
5) x = 5
6) x = 5
7) x = 14
8) x = 10
9) x = 7
10) x = 1

Bottom Section:
1) x = 2
2) x = 3