You could have simplified this in other ways, but I usually find it easier to get rid of the negative right away.
Now, with the first four inequalities in the table the interval notation is really nothing more than the graph without the number line on it. With the final four inequalities the interval notation is almost the graph, except we need to add in an appropriate infinity to make sure we get the correct portion of the number line.
They only get a parenthesis. We need to give one final note on interval notation before moving on to solving inequalities.
Always remember that when we are writing down an interval notation for an inequality that the number on the left must be the smaller of the two. We will use the following set of facts in our solving of inequalities.
We can however, write down an equivalent set of facts for the remaining three inequalities. These are nearly the same facts that we used to solve linear equations. The only real exception is the third fact. Now multiply both sides by 2 and by We will start off with inequalities that only have a single inequality in them.
This means that our solutions will, in most cases, be inequalities themselves. Example 1 Solving the following inequalities.
Give both inequality and interval notation forms of the solution. So, here is the inequality notation for the inequality. The process here is similar in some ways to solving single inequalities and yet very different in other ways.
Example 2 Solve each of the following inequalities. Give both inequality and interval notation forms for the solution. Our first step in this case will be to clear any parenthesis in the middle term.
The only thing that we need to remember here is that if we do something to middle term we need to do the same thing to BOTH of the out terms. One of the more common mistakes at this point is to add something, for example, to the middle and only add it to one of the two sides.
We will then proceed as we did in the first part.Page 1 of 2 Chapter 5 Quadratic Functions GRAPHING SYSTEMS Graph the system of inequalities. 7 and Parade Magazine ORESTRY Sawtimber a. A linear equation is any equation involving one or two variables whose exponents are one.
In the case of one variable, one solution exists for the equation. Mathematics Enhanced Scope and Sequence – Algebra II Virginia Department of Education © 7 Quadratic-Quadratic System Exploration 1.
Given the system. Try these by putting in numbers from the number line (in the pink, and not in the pink) to make sure you understand it!
Note that we will address Linear Inequalities in Two Variables in the Coordinate System and Graphing Lines Including Inequalities section here.. Note that we will address Absolute Value and Inequalities in the Solving Absolute Value Equations and Inequalities section here. A linear equation is an equation that makes a line when graphed.
A linear inequality is the same type of expression with an inequality sign rather than an equals sign.
For example, the general formula for a linear equation is y = mx + b, where m is the slope and y is the intercept. Systems of Linear Inequalities - HW Sketch the solution to each system of inequalities. 1) Sketch the solution to each system of inequalities. 1).