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Algebra

Study Guide

Algebra makes up about 55% of the GED Math test. You need to solve linear equations, work with inequalities, understand functions, and manipulate polynomials.

1Solving Linear Equations

To solve a linear equation, isolate the variable on one side. Whatever you do to one side, do to the other. Work in reverse order of operations: undo addition/subtraction first, then multiplication/division.

Examples:

•2x + 5 = 13 → 2x = 8 → x = 4
•3(x - 2) = 12 → x - 2 = 4 → x = 6
•5x - 3 = 2x + 9 → 3x = 12 → x = 4
2Linear Inequalities

Solve inequalities like equations, but flip the inequality sign when you multiply or divide by a negative number.

Examples:

•2x + 1 > 7 → 2x > 6 → x > 3
•-3x ≤ 12 → x ≥ -4 (sign flips!)
3Slope and Linear Functions

The slope of a line measures its steepness. Slope = rise/run = (y₂ - y₁)/(x₂ - x₁). The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.

Examples:

•Points (1, 3) and (4, 9): slope = (9-3)/(4-1) = 6/3 = 2
•y = 3x + 2 has slope 3 and y-intercept (0, 2)
•y = -x + 5 has slope -1 and y-intercept (0, 5)
4Systems of Equations

A system of two equations with two variables can be solved by substitution or elimination. The solution is the point where the two lines intersect.

Examples:

•y = 2x + 1 and y = -x + 4: Set equal → 2x + 1 = -x + 4 → 3x = 3 → x = 1, y = 3
•Elimination: x + y = 5 and x - y = 1 → add equations → 2x = 6 → x = 3, y = 2
5Polynomials and Factoring

To factor a quadratic x² + bx + c, find two numbers that multiply to c and add to b. For ax² + bx + c, use the AC method or the quadratic formula.

Examples:

•x² + 5x + 6 = (x + 2)(x + 3)
•x² - 9 = (x + 3)(x - 3) [difference of squares]
•2x² + 7x + 3 = (2x + 1)(x + 3)
Key Formulas to Remember
1Slope: m = (y₂ - y₁) / (x₂ - x₁)
2Slope-intercept form: y = mx + b
3Point-slope form: y - y₁ = m(x - x₁)
4Quadratic formula: x = (-b ± √(b² - 4ac)) / 2a
5Difference of squares: a² - b² = (a+b)(a-b)
Test-Taking Tips
Always check your answer by plugging it back into the original equation.
On the GED, you can use the formula sheet — memorize how to USE formulas, not just the formulas themselves.
When you see 'greater than' or 'less than' on a graph, remember the inequality sign flip rule.
Word problems often translate to linear equations. Identify the unknown and write an equation.