Lesson 08 · Preserving Equality

SOLVING FOR X

Use inverse operations to isolate a variable while preserving equality. The equation may change form from step to step, but the values that make it true must stay the same.

Preserve Equality

An equation states that two expressions have the same value. When solving, apply an equivalent operation to both sides so that equality is preserved while the variable becomes easier to see.

Undo +a

Subtract a

Undo −a

Add a

Undo ×a

Divide by a

Undo ÷a

Multiply by a

Undo the outer operation first

In a simple equation such as 2x + 6 = 14, addition by 6 is the outer operation acting on 2x, so subtract 6 before dividing by 2. This reverse-order idea is useful for one- and two-step equations, but it is a structural strategy, not a universal acronym for every equation you will ever solve.

Equation Lab

Logic Router

Current State

2(x + 3) - 4 = 10

What is the best first step?

Check by Substitution

After solving, substitute the proposed value back into the original equation. If both sides evaluate to the same number, the value satisfies the equation.

2x = 82(4) = 8true

Reference & Check

Review the vocabulary, then test whether the solving ideas hold together.

Solving Equations Checkpoint1 / 3

To solve the equation "4x - 5 = 15", what should be your VERY FIRST step?

Continue into Integrated Algebra

Use the same equality-preserving ideas with lines, systems, inequalities, functions, and polynomials.

Next: Integrated Algebra