The Equation Balance Scale
Apply operations to both sides to isolate the variable. Watch the scale track equality at every step.
LEFT SIDE
$3x + 6$
=
RIGHT SIDE
$18$
Choose an operation above to apply to both sides.
One & Two Step Equations
Undo operations in reverse order: last operation applied is first undone. Addition ↔ Subtraction. Multiplication ↔ Division.
🎯 Interactive: Choose the right first step
📖 I Do — Two-step equation
Solve: $5x - 7 = 28$
1
Undo subtraction: add 7 to both sides → $5x - 7 + 7 = 28 + 7$ → $5x = 35$
2
Undo multiplication: divide both sides by 5 → $x = \frac{35}{5} = 7$
3
Check: $5(7) - 7 = 35 - 7 = 28$ ✓
✏️ You Do
Solve: $x + 8 = 15$
(enter the value of x)
Subtract 8 from both sides to isolate $x$.
Solve: $3x = 24$
Divide both sides by 3.
Solve: $2x + 5 = 19$
Subtract 5 first, then divide by 2.
$2x = 14$ → $x = 7$. Check: $2(7)+5=19$ ✓

🤔 Why do we undo addition before division when solving $2x + 5 = 19$? Describe the logic of reverse order.

Brackets & Negatives
Expand brackets first, then collect like terms, then isolate the variable. When dividing by a negative, the inequality direction flips (for equations, just divide and track the sign).
⚠️ Interactive: Negative coefficient checker
📖 I Do — Brackets then solve
Solve: $3(2x - 1) = 21$
1
Expand: $6x - 3 = 21$
2
Add 3: $6x = 24$
3
Divide by 6: $x = 4$
4
Check: $3(2 \times 4 - 1) = 3(7) = 21$ ✓
✏️ You Do
Solve: $-2x = 10$
Divide both sides by $-2$. Positive ÷ negative = negative.
Solve: $2(x + 4) = 18$
Expand first: $2x + 8 = 18$. Then solve normally.
$2x = 10$ → $x = 5$.
Solve: $4(x - 3) = 8$
Expand: $4x - 12 = 8$. Add 12, then divide by 4.

🤔 When you solve $-3x = 12$, why does $x$ become negative?

Variables on Both Sides
Collect all variable terms on one side and all constants on the other. Subtract the smaller variable term from both sides first.
🔄 Interactive: Which side for the variable?
📖 I Do — Variables both sides
Solve: $6x - 3 = 2x + 13$
1
Subtract $2x$ from both sides: $6x - 2x - 3 = 13$ → $4x - 3 = 13$
2
Add 3: $4x = 16$
3
Divide by 4: $x = 4$
4
Check left: $6(4)-3 = 24-3 = 21$. Check right: $2(4)+13 = 8+13 = 21$ ✓
✏️ You Do
Solve: $5x + 2 = 3x + 10$
Subtract $3x$ from both sides: $2x + 2 = 10$.
$2x = 8$ → $x = 4$. Check: $5(4)+2=22=3(4)+10$ ✓
Solve: $4x - 1 = 7x - 13$
Subtract $4x$: $-1 = 3x - 13$. Then add 13.
Solve: $8 - x = 2x - 7$
Add $x$: $8 = 3x - 7$. Add 7: $15 = 3x$. Divide by 3.

🤔 Does it matter which side you collect the variable terms on? Could you get $x$ on the right side instead? Would the answer change?

The Gym
Solve each equation. Enter just the value of the variable (e.g. enter 5, not x=5).
Mild
Score: 0/10 · Streak: 0 · XP: 0
💀
The Equation Master
// Three stages · Escalating complexity · Full algebraic solutions required
🔸 Stage 1 — Solve with Brackets
Solve and fully verify: $3(2x + 4) - 2(x - 1) = 30$
Show your working (expanded form):
Value of x:
🔶 Stage 2 — Variables Both Sides
Solve: $4(x + 3) = 2(x + 9) + 6$
Show both sides expanded and simplified:
Value of x:
🔺 Stage 3 — Word Problem to Equation
Two friends, Alex and Sam, are saving money. Alex has $\$40$ and saves $\$15$ per week. Sam has $\$10$ and saves $\$25$ per week. After how many weeks will they have the same amount?
Write the equation (let $w$ = weeks):
Solve for $w$:
Calculator Hacks
Use your calculator to verify solutions by substituting back into the original equation.