Use A Sign Chart To Solve The Inequality
If you’re struggling with solving an inequality or just want to make sure you’re doing it correctly, a sign chart can be a helpful tool. A sign chart, also known as a number line chart, is a visual representation of the inequality that allows you to easily find the solution. In this article, we’ll explain how to use a sign chart to solve an inequality.
What is an inequality?
An inequality is a mathematical statement that compares two values or expressions. It is written using symbols such as <, >, ≤ or ≥. For example, 2x + 1 > 5 is an inequality. The solution to an inequality is a range of values that make the inequality true.
How to create a sign chart
To create a sign chart, you need to identify the critical points of the inequality. These are the points where the expression on each side of the inequality changes sign. For example, if the inequality is x(x-2)(x+3)≤0, the critical points are x=0, x=2, and x=-3.
Next, you need to plot these critical points on a number line. You should include all the critical points, even if they are not part of the solution. For example,
Now, you need to test a point from each interval on the number line to determine whether the expression is positive or negative in that interval. You can use any point in the interval, but it’s usually easiest to use a point close to the critical point. For example, if we test x=-4 in the first interval, x=-1 in the second interval, and x=1 in the third interval, we get:
- x=-4: (-4)(-6)(-1) < 0, which means the expression is negative
- x=-1: (-1)(-3)(2) > 0, which means the expression is positive
- x=1: (1)(-1)(4) < 0, which means the expression is negative
Finally, you can use the sign chart to identify the solution to the inequality. Any interval where the expression is negative is part of the solution. In the example above, the solution is:
x < -3 or 0 < x < 2
Why use a sign chart?
A sign chart can be a helpful tool when solving inequalities, especially when the expression is complex or has multiple critical points. It provides a visual representation of the inequality that makes it easier to identify the solution. Additionally, using a sign chart can help you avoid common mistakes such as forgetting to reverse the inequality when multiplying or dividing by a negative number.
Conclusion
If you’re struggling with solving an inequality or just want to make sure you’re doing it correctly, a sign chart can be a helpful tool. By identifying the critical points, plotting them on a number line, testing a point in each interval, and using the sign chart to identify the solution, you can solve inequalities with confidence.