Systems of Equations and Inequalities In previous chapters we solved equations with one unknown or variable. We will now study methods of solving systems of equations consisting of two equations and two variables. Represent the Cartesian coordinate system and identify the origin and axes. Given an ordered pair, locate that point on the Cartesian coordinate system.
Writing inequalities algebra Absolute value inequalities Video transcript A carpenter is using a lathe to shape the final leg of a hand-crafted table. A lathe is this carpentry tool that spins things around, and so it can be used to make things that are, I guess you could say, almost cylindrical in shape, like a leg for a table or something like that.
In order for the leg to fit, it needs to be millimeters wide, allowing for a margin of error of 2.
Now, they want us to write an absolute value inequality that models this relationship, and then find the range of widths that the table leg can be. So the way to think about this, let's let w be the width of the table leg.
So if we were to take the difference between w andwhat is this? This is essentially how much of an error did we make, right? If w is going to be larger thanlet's say it'sthen this difference is going to be 1 millimeter, we were over by 1 millimeter.
If w is less thanit's going to be a negative number. If, say, w wasminus is going to be negative 1. But we just care about the absolute margin.
So we just really care about the absolute value of the difference between w and This tells us, how much of an error did we make? And all we care is that error, that absolute error, has to be a less than 2.
And I'm assuming less than-- they're saying a margin of error of 2.
So this is the first part. We have written an absolute value inequality that models this relationship. And I really want you to understand this. All we're saying is look, this right here is the difference between the actual width of our leg and Now we don't care if it's above or below, we just care about the absolute distance fromor the absolute value of that difference, so we took the absolute value.
Now, we've seen examples of solving this before. So let me write this down. So this means that w minus has to be less than 2. So let's solve each of these. If we add to both sides of these equations, if you add and we can actually do both of them simultaneously-- let's add on this side, too, what do we get?
What do we get? The left-hand side of this equation just becomes a w-- these cancel out-- is less than or equal to plus 2.Write a compound inequality that the graph could represent.
Download png. Ask for details A compound inequality contains at least two inequalities that are separated by either "and" or "or". [-1, 3) The graph of the compound inequality represents the intersection of the graph of the inequalities.
1 vote 1 vote Rate! Rate! Thanks. 1 /5(4). Graphing inequalities on either a number line or in the coordinate plane (with x and y axes) helps to visually represent several forms of inequalities: The graph of a linear inequality produces a region on the coordinate plane with a boundary line.
Every point in that region is a solution of the inequality. Number lines help make graphing the union of two inequalities a breeze!
This tutorial shows you how to graph two inequalities on the same number line and then find the union. Check it out! In an inequality, one side of the inequality can be larger or smaller than the quantity on the other side. The math symbols, and ≥ provide information about the relative sizes of the two expressions.
b. Solve word problems leading to inequalities of the form px + q > r or px + q. How Do You Graph an Inequality or an Infinite Set on a Number Line? Number lines are really useful in visualizing an inequality or a set.
In this tutorial, you'll see how to graph .