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Equations
Practice

⬅️ Solve equations by moving terms across the equals sign

💡 When a term moves over, its sign flips: + becomes −, − becomes +

✖️ Solve equations using cross multiplication

💡 If a/b = c/d, then a × d = b × c

🔷 Expand brackets then solve

💡 Distributive law: a(b + c) = ab + ac

🏆 Solve challenging equations — brackets, fractions, and variables on both sides

📋 10 questions per round · pick or type your answer

⬅️ Moving Over (Transposition)

Move any term to the other side of = and flip its sign.

•3x + 5 = 17
→3x = 17 − 5 = 12
→x = 12 ÷ 3 = 4

Negative constant example:

•4x + 6 = −2
→4x = −2 − 6 = −8
→x = −2

Variables on both sides:

•5x + 3 = 2x + 15
→5x − 2x = 15 − 3
→3x = 12 → x = 4
Move a term → flip its sign  |  + becomes −, − becomes +

✖️ Cross Multiplication

If a/b = c/d, multiply diagonally: a × d = b × c.

•x/3 = 8/2
→2x = 3 × 8 = 24
→x = 12

Linear numerator:

•(2x + 1)/3 = 5
→2x + 1 = 15
→2x = 14 → x = 7
a/b = c/d  →  a × d = b × c

🔷 Expanding Brackets (Distributive Law)

a(b + c) = ab + ac — multiply the outer term by each term inside. Watch signs carefully with negatives!

•2(x + 3) = 14
→2x + 6 = 14
→x = 4

Negative multiplier — sign changes on both terms inside:

•−3(x − 2) = 9
→−3x + 6 = 9
→−3x = 3 → x = −1

Brackets on both sides:

•2(x + 1) = 3(x − 2)
→2x + 2 = 3x − 6
→8 = x → x = 8
a(b + c) = ab + ac  |  −a(b + c) = −ab − ac  |  −a(b − c) = −ab + ac
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