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Linear Expressions: Simplify Without Losing Structure

SAT MathAlgebraFoundation

Combine like terms, distribute accurately, and preserve equivalence.

What you need to know

  • Like terms have identical variable parts.
  • Distribute multiplication to every term inside parentheses.
  • A minus sign before parentheses changes every sign inside.
  • Equivalent expressions produce the same value for every allowed input.

The AYLOTI method

  1. Distribute first.
  2. Group variable terms and constant terms.
  3. Combine coefficients carefully.
  4. Check by substituting a simple value such as x = 2.

AYLOTI • Sir Hunain Zia • SAT Score 1594/1600 • 154 Total A Grades (Personal), 11 World Records, 7 Distinctions

Worked example

Simplify 3(2x − 5) − 2(x + 4).

  1. Distribute: 6x − 15 − 2x − 8.
  2. Combine x-terms: 4x.
  3. Combine constants: −23.

Answer: 4x − 23.

Common SAT traps

  • Distributing only to the first term.
  • Forgetting that −2(x + 4) gives −2x − 8.
  • Combining unlike terms.
Quick check

Simplify 5(x − 2) + 3x.

8x − 10.

Before you move on

  • Explain the core rule without looking back.
  • Redo the worked example using your own steps.
  • Write the trap you are most likely to fall for.
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