Use the quiz below to remind yourself of how to represent sets of numbers on a number line. You may find the definitions you wrote down last lesson helpful.[br][br]You will see "correct" displayed when you have selected the correct answer. Use the slider to switch between the different types of inequality.[br][br]Move on when you are happy
If you were asked to solve the inequality [math]x+6<10[/math] you could do so algebraically by subtracting 6 from both sides to give [math]x<4[/math][br][br]We can then represent the set of solutions on a number line:[br] [img]data:image/png;base64,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[/img][br] [img]data:image/png;base64,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[/img][br][br]We could also choose to solve this graphically, by plotting the graphs of the two lines:[br] [math]y=x+6[/math] and [math]y=10[/math][br][br]and determining for which values of [math]x[/math] the line [math]y=x+6[/math] is less than (below) the line [math]y=10[/math], (which side of the point of intersection)[br][br]Solve the equations on your sheet algebraically, and use the plotting tool below to verify your answers
What if you were asked to solve [math]6-x>2[/math]?[br][br]Does your answer correspond with what the graph shows you? What is different about this example?[br][br]Complete the next set of questions, try to explain what is happening, using the graphs to help describe why.