Unit 1 Math Study Group: Equations, Inequalities, and Literal Equations

Vocabulary terms and core concepts covering linear equations, solution types, literal equations, inequalities, and absolute value equations from the EdGems Course 3AC Unit 1 Review.

Solution types

The three possible classifications for solutions to a linear equation: one solution, no solution, or infinitely many solutions.

One solution

An outcome where an equation simplifies to exactly one true value for the variable, such as in $-7k + 1 = -13$ or $-5p + 3 = -17$.

No solution

An outcome where no real value can satisfy the equation, which occurs when an equation simplifies to a contradiction or when an isolated absolute value equals a negative number (e.g., $4|x| + 14 = 12$).

Infinitely many solutions

An outcome where any value substituted for the variable makes the statement true because both sides simplify to identical expressions, such as $3(2r + 1) = 6r + 3$.

Literal equation

An equation containing multiple variables that is rearranged to isolate a specific indicated variable (for example, solving $P = 2l + 2w$ for $l$ or $A = bh$ for $h$).

Isolating the variable

The process of rearranging an equation using inverse operations so that a specified variable is completely alone on one side.

Inequality

A mathematical statement comparing expressions with order symbols (such as $4x + 1 \le -3$), whose solution set is represented on a number line using shading and circles.

Open and closed circles

Visual markers used on a number line to graph inequalities: an open circle indicates that the boundary value is not included, while a closed circle indicates that the boundary value is included.

Compound inequality

An inequality that connects three expressions with two inequality signs, such as $10 > 2x + 6 > x + 5$ or $12 > 2x + 4 > x + 3$.

Absolute value equation

An equation containing an absolute value expression (such as $11 - |n + 5| = 8$ or $4|x| + 14 = 12$) that can have two solutions, one solution, or no solution.

Study plan readiness levels

The three self-assessment categories used to evaluate skill proficiency: READY (can do alone), ALMOST (sometimes needs help), and NEED TO STUDY (needs practice).