Objective: Solve linear equations by isolating the variable and display the solution(s) on a number line.
An inequality is a number sentence containing "is greater than," "is less than," "is greater than or equal to," "is less than or equal to," or "is not equal to symbols."
Any value for the variable that makes an inequality true is called a solution. As there are often more than one solution to inequalities, the set of all solutions is called the solution set.
Because the set of solutions for an inequality like x < 2 is too numerous to list, it is helpful to make a drawing, or graph, that represents all the solutions. We draw graphs of inequalities in one variable on number lines by shading all points that are solutions. Watch the video to learn more about graphing inequalities.
The solutions to inequalities are often not as obvious as simply x < 2. Consider the example 3x - 4 < 5, where the set of solutions for x are not apparent. To solve inequalities we can use the addition principle and multiplication principle that we used when solving equations. But be careful, because these principles for inequalities may not work the same way as they do for equations. Watch the video below to see in which ways these principles with inequalities are the same as with equations and in which ways they differ.
Complete the worksheet attachment below and then check your answers using the solutions attachment. Once you have completed these exercises, click the link to advance to the next lesson.