If 3(x - 4) = 2x + 5, what is the value of x?

x = 17. Distribute to get 3x - 12 = 2x + 5, then subtract 2x and add 12 to both sides.

What does it mean for a linear equation to have 'no solution'?

A linear equation has no solution when simplification yields a false statement (e.g., 3 = 5), meaning the lines are parallel and never intersect.

What does it mean for a linear equation to have 'infinitely many solutions'?

A linear equation has infinitely many solutions when simplification yields a true statement for all values (e.g., 5 = 5), meaning both sides are identical expressions.

What is the slope-intercept form of a linear equation and what does each variable represent?

y = mx + b, where m is the slope (rate of change) and b is the y-intercept (the value of y when x = 0).

How do you find the slope of a line passing through points (x₁, y₁) and (x₂, y₂)?

Use the slope formula: m = (y₂ - y₁) / (x₂ - x₁). This measures the rise over run between the two points.

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SAT Algebra & Functions Mastery

Master the essential Algebra & Functions concepts tested on the SAT with these 35 targeted flashcards. Covering linear equations, systems of equations, functions, quadratics, and inequalities, this deck prepares students for the most frequently tested algebraic topics. Perfect for self-study, tutoring sessions, or last-minute SAT review.

35 cards Intermediate Linear Equations & Expressions Systems of Equations Quadratics & Polynomials Functions Inequalities & Absolute Value

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