MKMathematics Knowledge

Linear Equations & Algebra

Isolate the variable — that's the entire job in linear algebra, and every ASVAB MK question in this category follows the same rules.

Formula Reference

  • Solve for x: do the same operation to both sides of the equation
  • Distributive property: a(b + c) = ab + ac
  • Combining like terms: 3x + 5x = 8x (only combine terms with the same variable and exponent)
  • Two-step equation: undo addition/subtraction first, then multiply/divide
  • Slope-intercept form: y = mx + b (m = slope, b = y-intercept)
  • Solving for two variables: use substitution or elimination

What the ASVAB is actually testing

Linear algebra questions on MK always have one goal: solve for an unknown. The variable might be x, it might be in a formula, or it might be embedded in a geometry calculation. The ASVAB doesn't test advanced algebra — no quadratics, no logarithms. It tests whether you can isolate a variable using the basic rules of equality.

If you can reliably do that, you'll get full credit on this topic.

Isolating the variable: the one principle

Whatever you do to one side of an equation, you must do to the other. That's it. Every multi-step algebra problem is just that rule applied repeatedly until the variable stands alone.

Undo operations in reverse order of operations. If the equation is 3x − 7 = 14, addition/subtraction happened last (the −7), so undo it first. Then undo the multiplication (the 3×).

Distributing negatives: where most errors happen

When a negative is outside parentheses, it applies to every term inside. −3(x − 4) is not −3x − 12. The double negative gives you −3x + 12. This is the single most common algebra mistake on the ASVAB.

Write out the distribution step explicitly — don't do it in your head.

Slope-intercept form

The ASVAB tests y = mx + b mostly by asking for the slope, y-intercept, or a specific y-value given an x. Know that m is slope (rise over run) and b is where the line crosses the y-axis. Plug in and compute — there's nothing tricky here as long as you don't mix up which constant is which.

Connection to other topics

Linear algebra connects to every MK topic that uses formulas — geometry perimeter, area, and volume problems are often algebra in disguise: you're given one value and asked to solve for a dimension. Fractions and decimals also appear as coefficients, so combine this topic with fractions-decimals for the full picture.

Common Pitfalls

  • Performing an operation on one side but forgetting to apply it to the other side
  • Sign errors when distributing a negative: −2(x − 3) = −2x + 6, NOT −2x − 6
  • Combining unlike terms: 3x + 4 cannot be simplified (x and a constant are different)
  • Misidentifying slope: in y = 3x + 2, the slope is 3, not 2
  • Stopping after finding one variable when the problem asks for the other

Worked Examples

Q1: Solve for x: 3x − 7 = 14

Answer: Add 7 to both sides: 3x = 21. Divide both sides by 3: x = 7

Q2: Solve for x: 2(x + 5) = 24

Answer: Distribute: 2x + 10 = 24. Subtract 10: 2x = 14. Divide by 2: x = 7

Q3: If 4x + 3 = 2x + 11, what is x?

Answer: Subtract 2x from both sides: 2x + 3 = 11. Subtract 3: 2x = 8. Divide by 2: x = 4

Q4: A line has equation y = 2x − 5. What is the y-value when x = 4?

Answer: y = 2(4) − 5 = 8 − 5 = 3

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