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Question 1 of 4
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Representing Inequalities on the Number Line
Greater than or equal (≥)
First, change the inequality sign into an equal sign and find the x values using cross method
x+3 |
= |
0 |
x+3 -3 |
= |
0 -3 |
x |
= |
-2 |
x-4 |
= |
0 |
x-4 +4 |
= |
0 +4 |
x |
= |
4 |
Mark these 2 points on a number plane. Use filled dots since the sign used is ≤
Next, test a point to determine which part of the number line is covered by x
Try x=-5
x2-x-12 |
≤ |
0 |
(-5)2-(-5)-12 |
≤ |
0 |
Substitute x=-5 |
25+5-12 |
≤ |
0 |
18 |
≤ |
0 |
This is not true, which means -3≤x≤4
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Question 2 of 4
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The cross method is a factorisation method used for quadratics.
First, change the inequality sign into an equal sign and find the x values using cross method
4+3x-x2 |
= |
0 |
-x2+3x+4 |
= |
0 |
Convert to standard form |
x2-3x-4 |
= |
0 |
Multiply the function by -1 |
x2-3x-4 |
= |
0 |
x-4 |
= |
0 |
x-4 +4 |
= |
0 +4 |
x |
= |
4 |
x+1 |
= |
0 |
x+1 -1 |
= |
0 -1 |
x |
= |
-1 |
Mark these 2 points on the x axis.
Next, substitute x=0 to the function to get the y intercept
y |
= |
4+3x-x2 |
y |
= |
4+3(0)-(0)2 |
Substitute x=0 |
y |
= |
4 |
Mark this point on the y axis.
Form a parabola by connecting the points
Since we are looking for y≥0, the values are on or above the x axis
This means that x is greater than or equal to -1 and less than or equal to 4
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Question 3 of 4
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The cross method is a factorisation method used for quadratics.
First, change the inequality sign into an equal sign and find the x values using cross method
2x2 |
= |
7x+4 |
2x2-7x-4 |
= |
0 |
Convert to standard form |
2x2-7x-4 |
= |
0 |
2x+1 |
= |
0 |
2x+1 -1 |
= |
0 -1 |
2x÷2 |
= |
-1÷2 |
|
x |
= |
-12 |
x-4 |
= |
0 |
x-4 +4 |
= |
0 +4 |
x |
= |
4 |
Mark these 2 points on the x axis.
Next, substitute x=0 to the function to get the y intercept
y |
= |
2x2-7x-4 |
y |
= |
2(0)2-7(0)-4 |
Substitute x=0 |
y |
= |
-4 |
Mark this point on the y axis.
Form a parabola by connecting the points
Since we are looking for y>0, the values are above the x axis
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Question 4 of 4
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The cross method is a factorisation method used for quadratics.
First, change the inequality sign into an equal sign and find the x values using cross method
-5x2+7x-2 |
≥ |
0 |
-5x2+7x-2 |
= |
0 |
5x-2 |
= |
0 |
5x-2 +2 |
= |
0 +2 |
5x÷5 |
= |
2÷5 |
|
x |
= |
25 |
x-1 |
= |
0 |
x-1 +1 |
= |
0 +1 |
x |
= |
1 |
Mark these 2 points on the x axis.
Next, substitute x=0 to the function to get the y intercept
y |
= |
-5x2+7x-2 |
y |
= |
-5(0)2+7(0)-2 |
Substitute x=0 |
y |
= |
-2 |
Mark this point on the y axis.
Form a parabola by connecting the points
Since we are looking for y≥0, the values are above the x axis