They are sometimes written with the symbols for “and” and for “or”.įor example, \(x\leq -1\cup\text\), move up 3 units and right 1 unit to \((1,4)\). Nice work!Ī compound inequality is two or more inequalities that are joined together with either “and” or “or”. Since \(x\) is greater than or equal to -4, the line extends to the right, showing all possible solutions for \(x\). Let’s take a look at the number line for \(x\geq -4\):Īs you can see, the circle above -4 is closed to indicate that -4 is part of the solution set. When you finish, resume the video, and we’ll go over the graph together. Pause the video here, draw a number line, and try this one yourself. Graph the solution set for the inequality \(x\geq -4\). Since \(x\) is less than or equal to 1, we need to draw the line to the left of 1. Next, starting from 1, draw a line to indicate all other possible solutions for \(x\). The circle is closed to indicate that 1 is part of the solution set for this inequality. Let’s graph the inequality on a number line.įirst, find 1 on the number line and draw a shaded circle above it on the number line. This line shows that the possible solutions for \(x\) are all numbers greater than -3. From -3, there is a line extending to the right with an arrow at the end. Remember, this means that -3 is not part of the solution set because \(x\neq -3\). Notice that there is an open circle directly above -3 on the number line. Let’s take a look at the number line together. Pause the video here, draw a number line, and see if you can graph this one yourself. If \(x\) is greater than -3, then all possible solutions for \(x\) have to be numbers that are greater than -3. Graph the solution set for the inequality \(x>-3\). The arrow indicates that even though the number line ends at -10, there are an infinite number of solutions (numbers smaller than -10) that could make this inequality true. Notice that the line extends to the left of 5 with an arrow at the end. Since \(x\) is less than 5, we need to draw a line to the left of 5. Next, draw a line on the number line to indicate the possible solutions for \(x\). The value for \(x\) is less than 5, not equal to it. We leave this circle open to indicate that 5 is not part of the solution set for this inequality. We can illustrate this on a number line.įirst, find 5 on the number line and draw an open circle above 5. If \(x\) is less than 5, then all possible solutions for \(x\) have to be numbers that are smaller than 5. Let’s take a look at an example: \(x \lt 5\). These graphs help illustrate all possible solutions, or the solution set, for the inequality. Solutions to inequalities are graphed on number lines and coordinate planes, depending on how many variables are in the inequality. For instance, one possible solution to \(x\lt 15\) is 5 because 5 is less than 15. Solutions are numbers we can replace the variables for in inequalities that make them true. Likewise, \(x \geq 6\) means that the value of \(x\) is greater than or equal to 6.
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