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The number two is shaded on both the first and second graphs. This is how we will show our solution in the next examples. Just as the United States is the union of all of the 50 states, the solution will be the union of all the numbers that make either inequality true.There are no numbers that make both inequalities true. There are no numbers that make both inequalities true. There are no numbers that make both inequalities true. To find the solution of the compound inequality, we look at the graphs of each inequality, find the numbers that belong to either graph and put all those numbers together.We will use the same problem solving strategy that we used to solve linear equation and inequality applications.
The bill for Normal Usage would be between or equal to .06 and 1.02.
For the compound inequality \(x−3\) and \(x\leq 2\), we graph each inequality. The numbers that are shaded on both graphs, will be shaded on the graph of the solution of the compound inequality.
See We can see that the numbers between \(−3\) and \(2\) are shaded on both of the first two graphs. The number \(−3\) is not shaded on the first graph and so since it is not shaded on both graphs, it is not included on the solution graph.
\[\begin & & \ & & \ \end \nonumber\] To solve a compound inequality means to find all values of the variable that make the compound inequality a true statement.
We solve compound inequalities using the same techniques we used to solve linear inequalities.