Definition
Substitution
Substitution puts a stated value or equal expression wherever the matching variable or expression occurs.
Continue from this idea into connected AXIO math.
Defining relationship
Replace the letter everywhere, but keep the operation frame.
In mathematics, substitution uses an equality to exchange every required occurrence of one variable or expression for the stated replacement, without altering the surrounding operations.
- 1
given value
- 2
original expression
- 3
replace x everywhere; keep the operation frame
- 4
then evaluate
- Every x is replaced
- Multiplication and addition stay in place
What it means
A variable is a place that can hold a value. Substitution puts the given value into that place everywhere it appears. Use parentheses for a negative value or a multi-part expression so the original operations stay in the right order.
Remember it
Replace the letter everywhere, but keep the operation frame.
Example
Substitute x = −3 into x² + 2x. Write (−3)² + 2(−3). This is 9 − 6 = 3. The parentheses keep the negative value together.
Watch for
For x = −3, x² becomes (−3)² = 9. Writing −3² gives −9 because the exponent acts before the outside negative sign.
Common mix-up
Substitution is the replacement step. Evaluation is the calculation that may follow after the replacement.
Exact meaning
In mathematics, substitution uses an equality to exchange every required occurrence of one variable or expression for the stated replacement, without altering the surrounding operations.