A system of inequalities is two or more inequalities that pertain to the same problem.
We first need to review the symbols for inequalities: There are endless solutions for inequalities. In light of this fact, it may be easiest to find a solution set for inequalities by solving the system graphically.
In doing so, you can treat the inequality like an equation. This will form the "boundary" of the inequality -- on one side of the line the condition will be true, on the other side it will not.
Review how to graph a line here. Notice that it is true when y is less than or equal to. In step 3 we plotted the line the equal-to caseso now we need to account for the less-than case. Since y is less than a particular value on the low-side of the axis, we will shade the region below the line to indicate that the inequality is true for all points below the line: Plug in a point not on the line, like 0,0.
Verify that the inequality holds. We have shaded the correct side of the line. Find all values of x and y that satisfy: Notice that this inequality is already in the slope-intercept form. I will replace the given inequality symbol for the equal symbol to plot the line.
Now plot that line as shown: Since this is a case where the inequality is true for y values greater than or equal to something, we have shaded the area above the line.
Again, select any point above the graph line to make sure that it will satisfy or reveal a TRUE statement in terms of the original inequality. Since that point was above our line, it should be shaded, which verifies our solution. Multiple inequalities - a system of inequalities A system of inequalities has more than one inequality statement that must be satisfied.
Graphically, it means we need to do what we just did -- plot the line represented by each inequality -- and then find the region of the graph that is true for BOTH inequalities. For the two examples above, we can combine both graphs and plot the area shared by the two inequalities.
What is the solution set?Course 1 • Chapter 8 Functions and Inequalities NAME _____ DATE _____ PERIOD _____ Copyright © The M cGraw-Hill Comp. Page 1 of 2 Solving an Inequality with a Variable on One Side Solve 5y º 8 Write original inequality. 5y graph at the right.
1. Write a compound inequality that represents each phrase. Graph 2 of the 5 problems on your paper. 2. Solve each compound inequality.
Graph 2 of the 5 problems on your paper.
3. Write each interval as an inequality. Graph 2 of the 5 problems on your paper. 4. Write each inequality or set in inter Learn with flashcards, games, and more — for free.
With "or" inequalities, we graph the numbers that satisfy either inequality, or both at the same time. In other words, we graph the combination, or union, of both inequalities. Let's start by looking at an "or" example in depth.
Interval Notation and Linear Inequalities Linear Inequalities Linear Inequalities Write the inequality algebraically. (b) Graph the inequality on the real number line. (c) Write the inequality in interval notation. 1. x is greater than 5.
Write and graph a linear inequality that represents th situation. you have $48 to spend on music and downloads. Each album download costs $5 and each movie download costs $8.