Year 7 Maths Worksheets | Cazoom Maths Worksheets - Free Printable

To solve these linear equations, we need to isolate the variable $x$. This means we want to get $x$ by itself on one side of the equals sign.

Here is the general strategy:
1. Move the numbers: Use addition or subtraction to move the constant number (the one without an $x$) to the other side of the equation.
2. Isolate $x$: Use multiplication or division to get rid of the number attached to $x$.

Let's solve the equations step-by-step.

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Section A

*These equations are in the form $ax + b = c$.*

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

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

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

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

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

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

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

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

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

10) $4x + 7 = 9$
* Subtract 7 from both sides: $4x = 2$
* Divide by 4: $x = 0.5$

11) $8x + 11 = 15$
* Subtract 11 from both sides: $8x = 4$
* Divide by 8: $x = 0.5$

12) $4x + 17 = 18$
* Subtract 17 from both sides: $4x = 1$
* Divide by 4: $x = 0.25$

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Section B

*These equations have the number first, like $b + ax = c$, but the steps are the same.*

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

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

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

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

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

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

7) $23 = x + 8$
* Subtract 8 from both sides: $15 = x$ (or $x = 15$)

8) $28 = 3x + 1$
* Subtract 1 from both sides: $27 = 3x$
* Divide by 3: $9 = x$ (or $x = 9$)

9) $53 = 8x + 5$
* Subtract 5 from both sides: $48 = 8x$
* Divide by 8: $6 = x$ (or $x = 6$)

10) $13 = 11 + 4x$
* Subtract 11 from both sides: $2 = 4x$
* Divide by 4: $0.5 = x$ (or $x = 0.5$)

11) $7 = 8x + 3$
* Subtract 3 from both sides: $4 = 8x$
* Divide by 8: $0.5 = x$ (or $x = 0.5$)

12) $12 = 7 + 15x$
* Subtract 7 from both sides: $5 = 15x$
* Divide by 15: $x = 5/15$ which simplifies to $x = 1/3$

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Section C

*These equations involve subtraction, like $ax - b = c$.*

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

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

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

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

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

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

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

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

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

10) $2x - 1 = 2$
* Add 1 to both sides: $2x = 3$
* Divide by 2: $x = 1.5$

11) $4x - 8 = 10$
* Add 8 to both sides: $4x = 18$
* Divide by 4: $x = 4.5$

12) $15x - 2 = 3$
* Add 2 to both sides: $15x = 5$
* Divide by 15: $x = 5/15$ which simplifies to $x = 1/3$

Final Answer:
Section A
1) $x = 2$
2) $x = 7$
3) $x = 12$
4) $x = 4$
5) $x = 8$
6) $x = 3$
7) $x = 7$
8) $x = 7$
9) $x = 2$
10) $x = 0.5$
11) $x = 0.5$
12) $x = 0.25$

Section B
1) $x = 3$
2) $x = 3$
3) $x = 7$
4) $x = 12$
5) $x = 9$
6) $x = 8$
7) $x = 15$
8) $x = 9$
9) $x = 6$
10) $x = 0.5$
11) $x = 0.5$
12) $x = 1/3$

Section C
1) $x = 8$
2) $x = 11$
3) $x = 6$
4) $x = 6$
5) $x = 14$
6) $x = 3$
7) $x = 4$
8) $x = 13$
9) $x = 4$
10) $x = 1.5$
11) $x = 4.5$
12) $x = 1/3$