Algebra & Numerical Reasoning

Single-Variable Equations

Solving for X by isolating variables and combining like terms.

Applied problems are set in office scenarios: rental fees, travel distances, payroll calculations, and investment figures.

What the exam tests

Standard Linear Equations

Basic exercises requiring arithmetic to isolate X (e.g., 5x − 3x = 13 − 7).

Multi-Step Bracketed Equations

Equations with parentheses requiring bracket expansion before combining terms (e.g., 6(2x − 5) − 5x = 2x − 7 + 2).

Equations with Fractions

Problems where terms or the variable are part of a fraction. Use common denominators to simplify (e.g., (2x+1)/6 = 1/3).

Applied Word Problems

Translate text into a formula and solve. Examples include rental car fees, travel distance, and interest rate scenarios.

Formula Rearrangement

Manipulate rate formulas such as Speed (S = V × T) or Work (W = P × T) to solve for a missing variable.

Multiple-Choice Reverse Solving

Plug each answer choice back into the original equation to find the one that holds true. This is often faster than solving from scratch.

Algebraic Isolation

Key rules

  • ›Combine all X terms on one side and all constants on the other.
  • ›Use properties of equality: add, subtract, multiply, or divide the same value on both sides.
  • ›Expand brackets first by multiplying terms across parentheses before combining like terms.
  • ›To clear fractions, multiply every term on both sides by the common denominator.

Common traps

  • !Forgetting to distribute a negative sign when expanding brackets (e.g., −2(x − 3) = −2x + 6, not −2x − 6).

Word-to-Math Translation and Data Filtering

Key rules

  • ›Identify the unknown, assign it X, then build the equation from the problem's relationships.
  • ›Ignore irrelevant information such as names, dates, and unrelated figures. Extract only the numbers that define the equation.

Common traps

  • !Setting up the equation wrong is more costly than arithmetic errors. Read the problem twice before writing anything down.

Verification and Reasonableness

Key rules

  • ›Substitute your answer back into the original equation to confirm both sides are equal.
  • ›Use mental estimation to confirm the answer is in the right ballpark before finalizing.

Try one

Solve for x: 5x − 3x = 13 − 7.

A.2
B.3
C.6
D.10

Combine like terms: 2x = 6. Divide both sides by 2: x = 3.

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