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Linear Equations in One Variable

SAT MathAlgebraFoundation

Isolate the variable with legal inverse operations and verify the result.

What you need to know

  • Apply the same operation to both sides.
  • Clear fractions by multiplying by the least common denominator.
  • Distribute and combine before isolating when expressions are complex.
  • A solution must make the original equation true.

The AYLOTI method

  1. Simplify each side.
  2. Move variable terms to one side.
  3. Move constants to the other side.
  4. Divide by the remaining coefficient and check.

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

Worked example

Solve 4(2x − 3) + 5 = 3x + 18.

  1. Expand: 8x − 12 + 5 = 3x + 18.
  2. Combine and subtract 3x: 5x − 7 = 18.
  3. Add 7 and divide by 5: x = 5.

Answer: x = 5.

Common SAT traps

  • Changing a sign when moving a term without applying an operation to both sides.
  • Dividing before clearing grouped expressions.
  • Checking only the simplified equation rather than the original.
Quick check

Solve 7x + 4 = 25.

x = 3.

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.
Hunain Zia

Hunain Zia has previously achieved considerable success in the high-school educational stream, gaining a massive 154 Total A Grades and 7 Major Distinctions, a process in which he broke/ set 11 different world records, including the most A grades ever achieved, most subjects ever appeared in, most distinctions, gaining distinctions across two separate boards (Pearson Edexcel and CAIE) within the same year/ ever, and even 19 hours of constant examination. All records stand intact today. Hunain pursued his Honors Accounting Degree from the prestigious Bentley University, and then completed an LLB (in Honors) from University of London. Currently, he manages multiple social and commercial projects, has founded digital streams and works tirelessly in the education sector.

Educate A Change focuses on truly bringing change in the educational sector worldwide. All our courses are designed to ensure success, and provide complete preparation without requiring any other external material. Therefore, it takes away the expense of academies, books, past paper compilations and other miscellaneous items. Instead, by just the courses we offer, the student can prepare fully for the best grades in their CAIEs, Edexcel and other high-school exams. The earnings from our course-sales are invested in social projects and growing the free educational activities of Educate A Change.