Linear Inequalities: These are inequalities involving linear expressions, such as y < 2x + 3 or 3y ≥ 6x - 4.
Absolute Value Inequalities: These are inequalities involving absolute value expressions, such as |2x - 5| < 7 or |3y + 2| ≥ 10.
Solving Inequalities
To solve an inequality, follow these general steps:
Isolate the variable: If the variable is not already isolated, use inverse operations to isolate the variable on one side of the inequality.
Choose the correct inequality symbol: When solving, be mindful of whether the solution involves strict inequality (<, >) or inclusive inequality (≤, ≥).
When working with inequalities, it's important to remember the following properties:
Adding or subtracting a number: When adding or subtracting a number to both sides of an inequality, the inequality sign remains the same.
Multiplying or dividing by a positive number: When multiplying or dividing both sides of an inequality by a positive number, the inequality sign remains the same.
Multiplying or dividing by a negative number: When multiplying or dividing both sides of an inequality by a negative number, the inequality sign switches direction.
Study Guide
To master inequalities, it's important to:
Understand the meaning of inequality symbols and their relation to the number line.
Be able to solve linear and absolute value inequalities using appropriate methods.
Apply the properties of inequalities to simplify and solve problems.
Remember to review the properties of inequalities and practice solving various types of inequality problems to build a strong understanding of this topic.
Number and Operations: In grade 4, students used equivalent fractions to determine the decimal representations of fractions that they could represent with terminating decimals. Students now use division to express any fraction as a decimal, including fractions that they must represent with infinite decimals. They find this method useful when working with proportions, especially those involving percents. Students connect their work with dividing fractions to solving equations of the form ax = b, where a and b are fractions. Students continue to develop their understanding of multiplication and division and the structure of numbers by determining if a counting number greater than 1 is a prime, and if it is not, by factoring it into a product of primes.