Algebra 1 Module 2 - Topic 2 Flashcards

Solutions and Equations

• A solution to an equation is any variable value that makes the equation true.

Types of Solutions

• Infinite solutions occur when linear equations are created by equating two equivalent expressions.
• No solution arises in linear equations of the form ax + b, where both expressions have the same coefficient for x (a) but different constant terms (b).

Forms of Linear Equations

• The general form of a linear equation is expressed as y = ax + b, where 'a' represents the slope and 'b' indicates the y-intercept.
• The factored form is written as y = a(x - c), where 'a' is the slope and 'c' is the x-intercept.
• Standard form is represented as Ax + By = C, with A, B, and C as real numbers, and A and B not both equal to zero.

Special Types of Equations

• Literal equations are formulas or equations where variables represent specific measures.

Solving Inequalities

• Solving an inequality involves several steps: representing the problem as a function, writing it as an inequality, isolating the variable to find the solution, and interpreting the outcome.

Compound Inequalities

• A compound inequality combines two inequalities using "and" or "or."
• Conjunction refers to joint inequalities taking the form a < x < b, representing solutions that satisfy both conditions.
• Disjunction refers to inequalities structured as x < a or x > b, allowing for solutions that satisfy either inequality.