Write Equations and Inequalities 4 Mathematics are well

Write Equations and Inequalities #4 Mathematics are well and good but nature keeps dragging us around by the nose. ~Albert Einstein Section 1. 4

Tests

The Concept • Yesterday we talked about key words for arithmetic operators • Today we’re going to extend our knowledge of translating text into mathematics by incorporating equality and inequality symbols • Again, these skills are imperative to an easy navigation of the process of solving word problems

Equations vs. Inequalities In thinking about creating complete mathematical sentences, called either equations or inequalities, it behooves us to explore the dichotomy between these two items Equalities Inequalities = <, >, ≥, ≤ Solved by a finite quantity Solved by an infinite number of solutions Used in most settings Typically more realistic in use

Key Words As with our arithmetic operators, there are key words that aid in our efforts These are found on page 21 = is equal to < is less than > Is greater than Is less than or equal to is greater than or equal to the same as fewer than more than at most no more than at least, no less than

Examples • The difference of twice a number k and 8 is 12 • The quotient of a number p and 12 is at least 30 • The sum of 5 and a number r is no more than 15 • 4 more than twice a number k is no greater than the sum of k and 11

Examples • The product of 4 and a number w is at most 51 • The difference of a number z and 11 is equal to 35 • The sum of a number b and 3 is greater than 8 and less than 12 • The product of 9 and 4 lass than a number y is no more than 78

Checking Solutions Checking a solution to an equation means that it gets plugged into the equation For example, • Check if 3 is a solution to the following equation and inequality 4 x-3=12 5 -x>1

Example You are baking batches of cookies for a bake sale. Each batch takes 2. 5 cups of flour. You have 18 cups of flour. Can you bake 8 batches?

Most Important Points • Key Words

Homework 1. 4 • 1, 2 -10, 12 -45 X 3