Review Module: Linear Equations, Inequalities, and Slope (Vocabulary Flashcards)

Vocabulary flashcards covering key terms from linear equations, inequalities, and slope concepts in the notes.

Linear equation in one variable

An equation with one unknown whose value is a real number and the variable appears to the first power; can be written as ax + b = 0 with a ≠ 0.

Solution

A value of the variable that makes the equation true.

Distribute

Apply the distributive property to remove parentheses: a(b + c) = ab + ac.

Combine like terms

Add or subtract coefficients of terms that have the same variable and exponent on each side.

Isolate the variable

Move all variable terms to one side and constants to the other to solve; then solve for the variable.

Coefficient

The number multiplying the variable in a term of the form ax.

Constant

A term that is a fixed number, not involving the variable.

Conditional equation

An equation that is true for some values of the variable and false for others.

Contradiction

An equation that is false for every value of the variable.

Identity

An equation that is true for every allowed value of the variable (true for all x in its domain).

Linear inequality

An inequality in one variable of the form ax + b < c, ax + b ≤ c, ax + b > c, or ax + b ≥ c.

Interval notation

A notation to express a solution set as intervals on the real line, using parentheses or brackets and ∞.

Set-builder notation

A notation for a solution set written as { x | condition }.

Graph of a solution

Visualization of the solution set on a number line or coordinate plane.

Addition Property of Inequalities

If a ≤ b, then a + c ≤ b + c for any real c (adding the same number preserves the inequality).

Multiplication Property of Inequalities

If a ≤ b and c ≥ 0, then ac ≤ bc; if c < 0, the inequality direction reverses.

Slope

m = (y2 − y1) / (x2 − x1) for two distinct points P(x1,y1) and Q(x2,y2).

Non-vertical line

A line with two distinct x-values (x1 ≠ x2); its slope is defined.

Vertical line

A line where x is constant for all points; slope is undefined.

P and Q

Two distinct points used to determine a line's slope: P(x1,y1) and Q(x2,y2).

Identity vs. Contradiction vs. Conditional

Identity: true for all allowed x; Contradiction: false for all x; Conditional: true for some x values and false for others.

Real numbers

The set of all rational and irrational numbers; coefficients a, b, c are real numbers.

Check your answer

Verify that the proposed solution satisfies the original equation or inequality.