If 3x - 7 = 2x + 5, what is the value of x?

x = 12. Subtract 2x from both sides to get x - 7 = 5, then add 7 to both sides.

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

The equation simplifies to a true statement for all values of the variable, such as 0 = 0, meaning every real number is a solution.

How do you find the x-intercept of a linear equation in the form y = mx + b?

Set y = 0 and solve for x, giving x = -b/m.

If 5(2x - 3) = 4(x + 1) + 2x, how many solutions does this equation have?

No solution. Expanding gives 10x - 15 = 6x + 4, then 4x = 19... wait — expanding correctly: 10x - 15 = 4x + 4 + 2x = 6x + 4, so 4x = 19, x = 19/4. One unique solution.

What is the slope of a line passing through the points (2, 5) and (6, 13)?

Slope = (13 - 5)/(6 - 2) = 8/4 = 2.

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GRE Algebra & Equations Mastery

Master the essential algebra and equations concepts tested on the GRE Graduate Record Exam. This deck covers linear equations, quadratics, inequalities, systems of equations, and functions with 28 targeted flashcards designed to boost your Quantitative Reasoning score.

28 cards Intermediate Linear Equations & Expressions Quadratic Equations Systems of Equations Inequalities & Absolute Value Functions & Algebraic Manipulation

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