ACCUPLACER Elementary Algebra

ACCUPLACER Elementary Algebra focuses on assessing and enhancing foundational algebra skills essential for success in higher-level mathematics.

Operations with Integers and Rational NumbersSimplifying Algebraic ExpressionsSolving Linear Equations
Solving and Graphing Linear InequalitiesSystems of Linear EquationsPolynomials and Factoring
Budgeting and Shopping MathTravel and Distance ProblemsRecipe Scaling and Proportions
Mastering Multiple Choice QuestionsTime Management During the Test
Operations with Inte...Simplifying Algebrai...Solving Linear Equat...Solving and Graphing...Systems of Linear Eq...Polynomials and Fact...Budgeting and Shoppi...Travel and Distance ...Recipe Scaling and P...Mastering Multiple C...Time Management Duri...
Advanced Topics

Solving and Graphing Linear Inequalities

What Are Linear Inequalities?

Linear inequalities look like equations but use symbols like \( <, >, \leq, \geq \) instead of \( = \).

How to Solve

  • Treat them almost like equations, but remember:
    • When you multiply or divide both sides by a negative number, flip the inequality sign!
  • The solution is often a range of numbers.

Graphing Solutions

  • Use a number line.
  • Open circle for \( < \) or \( > \), closed circle for \( \leq \) or \( \geq \).
  • Shade the region representing all possible solutions.

Everyday Uses

Inequalities can show which options are within your budget, or how much time you have left before a deadline.

Key Formula

\[ax + b < c\]

Examples

  • Solve \( x - 4 > 2 \) gives \( x > 6 \); graph with an open circle at 6 and shade right.

  • Solve \( 2y + 3 \leq 7 \) gives \( y \leq 2 \); graph with a closed circle at 2 and shade left.

In a Nutshell

Solve inequalities and show solutions on a number line.

Key Terms

Inequality
A mathematical sentence that shows the relationship between quantities that are not equal.
Number Line
A line on which numbers are marked at intervals, used to illustrate solutions.
Next
Systems of Linear Equations