Sets of integers and real numbers can be represented on a [b]number line.[/b] [br]An [b]interval[/b] consists of all the numbers that lie within two certain boundaries. If the two boundaries, or fixed numbers, are included, then the interval is called a [b]closed interval.[/b] If the fixed numbers are not included, then the interval is called an [b]open interval.[/b]

By dragging the dots, and changing the type of inequality using the slider, fill in the missing information onto your sheet.

Using the worksheet, and the applet try to formulate definitions for the meaning of the symbols on your sheet. Discuss your definitions with your neighbour and amend if necessary.

An [b]integer[/b] is a whole number, positive, negative or zero.[br]List the set of [b]integer[/b] solutions which satisfy the inequalities given in question 3-6

A compound inequality is an inequality that combines two simple inequalities. [br]For example:[br][math]x<3\cup x>5[/math][br]The [math]\cup[/math] symbol means union, which can be interpreted as "or"[br]Use this information to answer questions 7 and 8

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.

The ability to solve a quadratic equation is not a pre-requisite for this activity, in part ii, a quadratic solver is available for those who do not know how to factorise, or prefer to use the quadratic formula.[br][br]Students should plot the graphs of two functions, where applicable, therefore there is no requirement to rearrange equations in part i, but there is an opportunity to do this, if the student wishes in part ii.

The general equation of a straight line is [math]y=mx+c[/math] where [math]m[/math] is the [color=#0000ff]gradient[/color], and [math]c[/math] the [color=#0000ff]y-intercept[/color].[br][br]The gradient can be calculated using [color=#ff0000][math]\frac{\Delta y}{\Delta x}[/math][/color], ([math]\Delta[/math] means change) it describes how [color=#0000ff]steep [/color]the slope of the line is, that is how much the [color=#0000ff]output [/color](y-value) increases, or decreases by, as a result of increasing the [color=#0000ff]input [/color](x-value) by 1.[br][br]The [color=#0000ff]y-intercept[/color] is the [color=#0000ff]y-coordinate[/color] of the point where the line meets the [color=#0000ff]y-axis[/color].

It is possible to draw comparisons between two functions, where one of them is a quadratic by plotting both of the functions, as we saw in lesson two.[br][br]If we wanted to find the set of solutions for which [math]x^2+3x+1[/math] < [math]1-x[/math][br]We will use the plotting tool to plot the graphs of  [math]y=x^2+3x+1[/math] and [math]y=1-x[/math][br][br]We can see that the blue function is less than the green function for values of [math]x[/math] between -4 and 0.[br]Try to imagine your [math]x[/math]-axis as a number line, we could represent the inequality on there like this:[br]                               [img]data:image/png;base64,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[/img]   [br]              [img]data:image/png;base64,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[/img][br][br]It is possible to represent this set of solutions using either inequality of interval notation as seen in lesson one.  So we could write the set of solutions to this inequality as -4 < [math]x[/math] < 0.[br][br]Similarly, if we were to write the set of solutions for which [math]x^2+3x+1[/math] > [math]1-x[/math], this would either be when [br][math]x[/math] < -4 or when [math]x[/math] > 0[br][br]

Complete the questions on the worksheet below, using the plotting tool to help.  Do a sketch of the number line, and write down the set of solutions to solve each inequality