Nevermind, I understand now. It seems so strange that you can multiply all three sides of an equality by the same number. I don't know what this property is called thought.Callumnc1 said:
For the continued inequality ##0 < |x - a| < \delta##, it's helpful to draw a sketch or two of the number line with a in an arbitrary position. x will then have to be somewhere inside a band of width ##2\delta## around a, but excluding a itself.Callumnc1 said:
The statement you started with is not an equation -- it's an inequality. There is a property of equations that you can multiply both sides of an equation by any nonzero number to get a new, equivalent equation. This idea can be extended to a continued equation.Callumnc1 said:
Amen! Mathematics is very cumulative. Anything that you were taught earlier will be used over and over in what follows. It can be very beneficial to review earlier material until it becomes natural to you.Mark44 said:
An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other. It uses symbols like >, <, ≥, and ≤.
To solve a linear inequality, you follow similar steps as solving a linear equation: isolate the variable on one side of the inequality sign. However, if you multiply or divide both sides by a negative number, you must reverse the inequality sign.
The different types of inequalities include linear inequalities, polynomial inequalities, rational inequalities, and absolute value inequalities. Each type involves different methods and rules for solving.
Sure! Consider the inequality 2x - 3 < 7. To solve it, add 3 to both sides to get 2x < 10. Then, divide both sides by 2 to get x < 5. So, the solution is x < 5.
Graphing an inequality means representing its solutions on a number line or coordinate plane. For a number line, you use open or closed circles to indicate whether endpoints are included. For a coordinate plane, you shade the region that represents all the solutions.