Inequalities Extra Worksheet #1
Section 1: In order to sketch an inequality you need to know the equation of the line associated with the
inequality. To find this replace the inequality sign (<, >, ≥ or ≤) with an equals sign (=)
i.e. The equation of the line associated with the inequality 3x + 2y > 5 is 3x + 2y = 5
Write the equation of the line associated with each of the following inequalities.
a) 2x + 4y < 3
ans 2x + 4y = 3
b) 3x – 2y ≥ 6
ans 3x – 2y = 6
c) 3y – x > 4
ans 3y – x = 4
d) 2x – y ≤ 5
and 2x – y = 5
If a ≤ or ≥ sign was used then it means that the points on the line are included in the solution set and a
solid line should be drawn
Eg 2x – 3y ≥ 3 draw a solid line
If a ≤ or ≥ sign was used then it means that the points on the line are included in the solution set and a
solid line should be drawn
Eg 2x – 3y ≥ 3 draw a solid line
If a < or > sign was used then it means that the points on the line are NOT included in the solution set
and a broken or dashed line should be drawn
Eg 2x – 3y ≥ 3 draw a broken line - - - - - For each of the inequalities above indicate whether a solid or broken line should be drawn.
a)
broken
b)
solid
c)
broken
d)
solid
Section 2 – In order to use your calculator to draw inequalities they have to be written in the form y = …
so you have to isolate the y variable.
Eg 4x + y = 2
In this case you just have to move the 4x to the right hand side of the
equation remembering to change its sign.
i.e. y = 2 – 4x
Rearrange these equations
a) 3x + y = 7
ans y = 7 – 3x
b) y – 3x = 4
ans y = 4 + 3x
c) y + 2x = 3
ans y = 3 – 2x
d) 4x + y = 5
ans y = 5 – 4x
If there is a number in front of the y you also need to divide by it
Eg 4x + 2y = 7
2y = 7 – 4x
move the 4x to the right
then divide by 2
y = (7 – 4x) / 2
Rearrange these equations
a) 3x + 2y = 5
ans
b) 4y – 2x = 7
ans
2y = 5 – 3x
y = (5 – 3x) / 2
4y = 7 + 2x
y = (7 + 2x) / 4
c) 3y – x = 4
ans
3y = 4 + x
y = (4 + x) / 3
d) 5y + 2x = 9
ans
5y = 9 – 2x
y = (9 – 2x) / 5
Sometimes an equation will look like 2x + 7y – 3 = 0
In this case both the 2x and the -3 need to be moved to the left hand side.
2x + 7y – 3 = 0 move the 2x and -3 to the right remembering to change the sign
7y = 3 – 2x
now divide by 7
y = (3 – 2x) / 7
Rearrange these equations
a) 3x + 5y + 2 = 0
ans
5y = -3x – 2
y = (-3x – 2) / 5
b) 2x + 5y – 7 = 0
ans
5y = 7 – 2x
y = (7 – 2x) / 5
c) -3x +2y + 9 = 0
ans
2y = 3x - 9
y = (3x – 9) / 2
d) -4x + 3y – 2 = 0
ans
3y = 4x + 2
y = (4x + 2) / 3
It is a bit more tricky if there is a –ve sign in front of the y as it needs to be moved first to make it
positive
Eg 3x – 2y = 7
move the -2y to the right
3x = 7 + 2y
now move the 7 to the left
3x – 7 = 2y
and finally, divide by 2
(3x – 7) / 2 = y
Rearrange these equations:
a) 2x – y = 5
ans
2x = 5 + y
2x – 5 = y OR y = 2x - 5
b) 3x – 2y = 7
ans
3x = 7 + 2y
3x – 7 = 2y
(3x – 7) / 2 = y or y = (3x – 7) / 2
c) 2x – 2y = 5
ans
2x = 5 + 2y
2x – 5 = 2y
(2x – 5) / 2 = y or y = (2x – 5) / 2
d) -3x – 2y = 3
ans
-3x = 3 + 2y
-3x – 3 = 2y
(-3x – 3) / 2 = y or y = (-3x – 3) / 2