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 (3x − 2)/4 = 7.
Show worked solution
× 4: 3x − 2 = 28. Add 2: 3x = 30, so x = 10. Check: 28/4 = 7. 3 forgets to multiply the 7 by 4; 12 divides only the 3x by 4, as if the bar did not cover the − 2; 30 forgets to divide by 3.
2 Solve (x + 4)/5 = (x − 2)/3. Fill in the line you get after multiplying both sides by 15, then give x.
Show worked solution
15 ÷ 5 = 3 and 15 ÷ 3 = 5: 3(x + 4) = 5(x − 2). So 3x + 12 = 5x − 10, 22 = 2x and x = 11. Check: 15/5 = 3 and 9/3 = 3.
3 Solve x/4 + x/6 = 15.
Show worked solution
× 12: 3x + 2x = 180, so 5x = 180 and x = 36. Check: 9 + 6 = 15.
Level 2 · Core
4 Solve x/2 − (x − 3)/5 = 3.
Show worked solution
× 10: 5x − 2(x − 3) = 30, so 5x − 2x + 6 = 30, 3x = 24 and x = 8. Check: 4 − 5/5 = 3. −1 forgets to multiply the 3 by 10; 12 writes −2(x − 3) as −2x − 6; 11 leaves out the bracket (5x − 2x − 3 = 30).
5 Solve the equation below. Give the LCD you multiply by, then x.
Show worked solution
LCD = 10. 2(2x + 3) − 10 = 5(x − 1), so 4x − 4 = 5x − 5 and x = 1. Check: 5/5 − 1 = 0 and 0/2 = 0.
6 Solve the equation below.
Show worked solution
× 12: 4(x + 1) − 3(x − 5) = 36, so 4x + 4 − 3x + 15 = 36, x + 19 = 36 and x = 17. Check: 18/3 − 12/4 = 6 − 3 = 3.
Level 3 · Challenge
7 Three statements:
1 x = 5 is the solution of (x − 3)/2 = (x + 1)/6.
2 Multiplying (5 − x)/3 − (x + 1)/2 = 1 by 6 gives 2(5 − x) − 3x + 3 = 6.
3 x = −5 is the solution of x/5 − 2 = (x − 4)/3.
Which statements are correct?
1 x = 5 is the solution of (x − 3)/2 = (x + 1)/6.
2 Multiplying (5 − x)/3 − (x + 1)/2 = 1 by 6 gives 2(5 − x) − 3x + 3 = 6.
3 x = −5 is the solution of x/5 − 2 = (x − 4)/3.
Which statements are correct?
Show worked solution
x = 5: 2/2 = 1 and 6/6 = 1 (1 ✓). −3(x + 1) = −3x − 3, so it should read 2(5 − x) − 3x − 3 = 6 (2 ✗). x = −5: −1 − 2 = −3 and −9/3 = −3 (3 ✓). 1 and 3.
8 The equation (x + a)/4 = (x − 1)/3 has the solution x = 7. Find a. Then use that value of a to solve (x + a)/4 = (x − 2)/3.
Show worked solution
(7 + a)/4 = 6/3 = 2, so 7 + a = 8 and a = 1. Then (x + 1)/4 = (x − 2)/3: 3x + 3 = 4x − 8, so x = 11. Check: 12/4 = 3 and 9/3 = 3.
9 Solve the equation below.
Show worked solution
× 6: 3(5 − x) − 2(2x − 1) = 24, so 15 − 3x − 4x + 2 = 24, 17 − 7x = 24, −7x = 7 and x = −1. Check: 6/2 − (−3)/3 = 3 + 1 = 4.