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Algebra › Substitution

Substitution

The simplest algebra move: replace a letter with a number, then work it out.

Substitute and evaluate

Pick an expression, slide the values, watch it become a number.

Step 1 — write the expression

2x + 3

Step 2 — replace each letter with a number

2(4) + 3

Step 3 — work it out

= 11

x4

Substitution is the simplest move in algebra: erase the letter, write a number in its place, then evaluate normally.

How it works

A formula is a recipe with blanks. Each letter is a blank waiting for a number. Substitution is the act of filling those blanks in.

For example, in 3x + 2, swap x for 4:

3(4) + 2 = 12 + 2 = 14

Use brackets when you substitute

Always wrap the value in brackets when you plug it in. It saves you from sign mistakes — especially when the number is negative.

In x² − 4 with x = −3:

(−3)² − 4 = 9 − 4 = 5

Without the brackets, you might square only the 3 and forget the minus. Brackets keep the negative attached to the number.

Two letters, two values

When an expression has more than one variable, substitute each one separately. In 3x − y with x = 5 and y = 2: 3(5) − (2) = 15 − 2 = 13.

Where you'll see this

  • Plugging numbers into a physics formula like v = u + at.
  • Checking your answer to an equation by substituting it back in.
  • Building a table of values to plot a graph.

Quick check

  1. If a = 2 and b = −5, what is a − b?
  2. Evaluate x² + 1 at x = −4.
  3. Evaluate 2(x + y) at x = 3, y = 7.

Answers: 7, 17, and 20.

Quick check

Evaluate x² + 1 at x = −4.

Quick check

Evaluate 2(x + y) at x = 3 and y = 7.