Solve inequalities using estimation

Learning Objectives Identify and interpret the four main inequality symbols (<, >, ≤, ≥). Define a variable and understand its role in an inequality. Use estimation to test different values for a variable in an inequality. Determine if a tested value makes an inequality statement true or false. Identify a range of possible solutions for a one-variable inequality through estimation. Explain what it means for an inequality to have multiple solutions. Translate simple word problems into one-variable inequalities. Ever wondered how many friends you can invite to a party if you only have 10 slices of pizza? 🍕 We use math to figure out situations like this! In this lesson, you'll learn how to solve problems where there isn't just one exact answer, but a range o...

TermDefinitionExample InequalityA mathematical statement that shows two expressions are not equal, using symbols like <, >, ≤, or ≥.The statement `x + 5 > 10` is an inequality, meaning 'x plus 5 is greater than 10'. VariableA letter (like x, y, or a) that represents an unknown number or a set of numbers in a mathematical expression or equation.In the inequality `x < 7`, 'x' is the variable. It can be any number less than 7. EstimationThe process of finding an approximate value or solution by making a reasonable guess and then testing it.To solve `y + 2 > 8`, you might estimate 'y' is 5, then test if `5 + 2 = 7` is greater than 8. Since it's not, you know 'y' must be larger. Solution (of an inequality)Any value(s) for the variable...

Understanding Inequality Symbols • $a < b$ means 'a is less than b' • $a > b$ means 'a is greater than b' • $a \le b$ means 'a is less than or equal to b' • $a \ge b$ means 'a is greater than or equal to b' These symbols tell us the relationship between two quantities. The 'mouth' of the symbol always opens towards the larger value. The line under $\le$ or $\ge$ means the numbers can also be equal. The Estimation Strategy: Test and Adjust To solve an inequality using estimation, substitute different numbers for the variable. Check if each number makes the inequality true. Start with a reasonable guess, then adjust your next guess higher or lower based on whether your first guess was too small or too large. Keep testing...