Understanding Linear Relationships

Linear equations and inequalities are the backbone of the SAT Math No Calculator section. They allow you to describe relationships with constant rates of change and are commonly used to solve real-life problems.

Solving Linear Equations

Linear equations have the form \( ax + b = c \). To solve for \( x \):

1. Isolate the variable by performing inverse operations.
2. Keep both sides balanced by doing the same operation to each side.
3. Check your solution by substituting back into the original equation.

Working with Inequalities

Inequalities use symbols like \( <, >, \leq, \geq \). Remember, multiplying or dividing both sides by a negative reverses the inequality sign!

Graphical Interpretation

Linear equations graph as straight lines, while inequalities represent regions above or below a line.

Real-World Connections

Linear equations and inequalities can represent budgeting, distance-rate-time problems, and basic economic models.