Solving Equations · grades 7–10

Solving Equations.

From the very first balance to multi-step solving — one-step, two-step, variables on both sides, distributing, and turning word problems into equations. With a balance-scale model, an animated step solver, and an engine-graded pad.

Meet equations

The balance and the solution.

1.1
Equation vs expression
A solution makes it true.
1.2
The balance rule
Do the same to both sides.
1.3
Inverse operations
Undo with the opposite.

One-step equations

One inverse operation.

2.1
Add to solve
x − a = b.
2.2
Subtract to solve
x + a = b.
2.3
Divide to solve
ax = b.
2.4
Multiply to solve
x/a = b.

Two-step equations

Undo in reverse order.

3.1
Two steps: ax + b = c
Undo + then ×.
3.2
ax − b = c
Add first, then divide.
3.3
x/a + b = c
Subtract, then multiply.
3.4
Two-step with negatives
Watch the signs.

Variables on both sides

Collect the x terms.

4.1
Variables on both sides
Collect the x terms.
4.2
Both sides with negatives
Keep the signs straight.
4.3
No solution or infinitely many
When the x terms cancel.
4.4
Both-sides mastery
Mixed practice.

Distribute & combine

Simplify first, then solve.

5.1
Distribute first
a(x + b) = c.
5.2
Combine like terms
Tidy one side first.
5.3
Distribute on both sides
Brackets everywhere.
5.4
Multi-step mastery
Everything together.

Apply

Word problems.

6.1
Translate to an equation
Words → symbols.
6.2
Solve a word problem
Set up and solve.
6.3
Number & money problems
Common setups.
6.4
Apply mastery
Mixed word problems.

Capstone

Pick the strategy.

C1
Pick the strategy
Every equation type.

Solving Equations.

Meet equations

Equation vs expression

The balance rule

Inverse operations

One-step equations

Add to solve

Subtract to solve

Divide to solve

Multiply to solve

Two-step equations

Two steps: ax + b = c

ax − b = c

x/a + b = c

Two-step with negatives

Variables on both sides

Variables on both sides

Both sides with negatives

No solution or infinitely many

Both-sides mastery

Distribute & combine

Distribute first

Combine like terms

Distribute on both sides

Multi-step mastery

Apply

Translate to an equation

Solve a word problem

Number & money problems

Apply mastery

Capstone

Pick the strategy