Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 Solve 3(x + 5) = 7x − 9.
Show worked solution
3x + 15 = 7x − 9. Subtract 3x: 15 = 4x − 9. Add 9: 24 = 4x, so x = 6. Check: 3(11) = 33 and 42 − 9 = 33. 1.5 moves −9 across without changing its sign; 3.5 multiplies only the x by 3 (3x + 5); 24 forgets to divide by 4.
2 Solve 4(x − 3) = x + 9. Fill in the line you reach after collecting the x-terms on the left and the numbers on the right, then give x.
Show worked solution
4x − 12 = x + 9. Subtract x and add 12: 3x = 21, so x = 7. Check: 4(4) = 16 and 7 + 9 = 16.
3 Solve the equation below.
Show worked solution
Subtract 2x: 4x − 7 = 25. Add 7: 4x = 32, so x = 8. Check: 48 − 7 = 41 and 16 + 25 = 41.
Level 2 · Core
4 Solve 18 − 2x = 4(x − 3).
Show worked solution
18 − 2x = 4x − 12. Add 2x: 18 = 6x − 12. Add 12: 30 = 6x, so x = 5. Check: 18 − 10 = 8 and 4(2) = 8. 1 moves −12 across without changing its sign (18 − 12 = 6x); 3.5 writes 4(x − 3) as 4x − 3; 15 subtracts 2x instead of adding it (18 = 2x − 12).
5 Solve 5 − 2(x − 4) = 3x − 7. Give the number term on the left once the bracket is expanded and collected, then x.
Show worked solution
5 − 2x + 8 = 3x − 7, so 13 − 2x = 3x − 7. Add 2x and 7: 20 = 5x, so x = 4. Check: 5 − 2(0) = 5 and 12 − 7 = 5.
6 Solve the equation below.
Show worked solution
6x + 15 = 2x + 2 + 1 = 2x + 3. Subtract 2x: 4x + 15 = 3. Subtract 15: 4x = −12, so x = −3. Check: 3(−1) = −3 and 2(−2) + 1 = −3.
Level 3 · Challenge
7 Three statements:
1 x = −1 is the solution of 3(x + 4) = 5 − (x − 3).
2 2(x − 1) + 3 = 2x + 1 is true for every value of x.
3 7 − 2(x + 1) = 7 − 2x + 2
Which statements are correct?
1 x = −1 is the solution of 3(x + 4) = 5 − (x − 3).
2 2(x − 1) + 3 = 2x + 1 is true for every value of x.
3 7 − 2(x + 1) = 7 − 2x + 2
Which statements are correct?
Show worked solution
With x = −1: 3(3) = 9 and 5 − (−4) = 9 (1 ✓). 2x − 2 + 3 = 2x + 1, the same on both sides for every x (2 ✓). −2(x + 1) = −2x − 2, so the right side should be 7 − 2x − 2 (3 ✗). 1 and 2.
8 When x = 5, the equation a(x − 2) = x + 4 is true. Find a. Then use that value of a to solve a(x − 2) = x + 10.
Show worked solution
a(5 − 2) = 5 + 4, so 3a = 9 and a = 3. Then 3(x − 2) = x + 10: 3x − 6 = x + 10, 2x = 16, x = 8. Check: 3(6) = 18 and 8 + 10 = 18.
9 Solve the equation below.
Show worked solution
Left: 12x − 8 − 6x + 15 = 6x + 7. Right: 2x + 18 − 3 = 2x + 15. So 6x + 7 = 2x + 15, 4x = 8 and x = 2. Check: 4(4) − 3(−1) = 19 and 2(11) − 3 = 19.