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Form 2 Mathematics Linear Inequalities Topical Video Questions and Answers
Graph each of the following inequalities:
(a)
3
(
1
2
x
-
1
y
y
)
≤
-
1
(b)
3
y
-
8
≥
-
6
x
(7m 7s)
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1.
Find the range of x if
2
≤
3
-
x
<
5
2.
Find all the integral values of x which satisfy the inequalities
2
(
2
-
x
)
<
4
x
-
9
<
x
+
11
3.
The diagram below shows the graphs of
y
=
3
10
x
-
3
2
,
5
x
+
6
y
=
30
and
x
=
2
. By shading the unwanted region, determine and label the region R that satisfies the three inequalities
y
≥
3
10
x
-
3
2
,
5
x
+
6
y
≥
30
and
x
≥
2
4.
Solve the following inequalities and represent the solutions on a single number line.
3
-
2
x
<
5
,
4
-
3
x
≥
-
8
5.
A mixed school can accommodate a maximum of 440 students. The number of girls must be at least 120 while the number of boys must exceed 150. Taking x to represent the number of boys and y the number of girls, write down all the inequalities representing the information above.
6.
Form the three inequalities that satisfy the given region R
7.
Solve the inequality
3
-
2
x
<
x
≤
2
x
+
5
3
and show the solution on the number line
8.
The sum of three consecutive odd integers is greater than 219. Determine the first three such integers.
9.
a). Solve the inequalities
2
x
-
5
>
-
11
and
3
+
2
x
≤
13
, giving the answer as a combined inequality. b). list the integral values of x that satisfy the combined inequality in (a) above.
10.
Given the inequalities
x
-
5
≤
3
x
-
8
>
2
x
-
3
a). solve the inequalities b). represent the solution on a number line
11.
Solve
4
≤
3
x
-
2
<
9
+
x
hence list the integral values that satisfies the inequality
12.
A school decided to buy at least 32 bags of maize and beans. The number of bags of maize were to be more than 20 and the number of bags of beans were to be at least 6. A bag of maize costs ksh. 2500 and a bag of beans costs ksh. 3500. The school had ksh. 100 000 to purchase the maize and beans. Write down all the inequalities that satisfy the above information.
13.
The diagram below shows a region R bounded by three lines L1, L2, and L3. Form the three inequalities that satisfy the given region R
14.
Solve the inequality
2
x
-
1
≤
3
x
+
4
<
7
-
x
15.
Write the simple statement below as a compound statement and illustrate your answer on a number line. x>2, x<6
16.
Write the simple statement given below as a compound statement and illustrate your answer on a number line.
x
<
-
4
,
x
≤
6
17.
Solve the inequality below and represent your solution on a number line.
6
-
1
2
x
>
12
18.
Solve the given inequality below and represent your solution on a number line. 3 – 2x < 17
19.
Solve the simultaneous inequality below and represent your answer on a number line. x + 3 > 5 x – 4 < 4
20.
Solve the simultaneous inequality given below and represent your answer on a number line.
-
1
2
x
–
2
≤
1
-
3
x
–
9
>
-
6
21.
Draw the regions which satisfy the following inequalities. x + y
≥
0 x < 2 y > 0
22.
Illustrate each of the following inequalities on a number line: (a) x < 7 (b) x > -3 (c) x = 0 (d) x =-5 (e) x < -10 (f) x < - 4 (g) x =- 6 (h) x < 2.5 (i) x =-1/2 (j) x =-2.3
23.
Write each of the following pairs of simple statements as a compound statement: (a) x > 2, x < 5 (b) x
≥
3, x < 6 (c) x
≥
1, x
≤
7 (d) x > - 4, x
≤
0 (e) x
≥
-
3, x
≤
-1
24.
Write each of the following pairs of simple statements into a compound statement and illustrate the answer on a number line: (a) x
≤
0.5, x
≥
0.1 (b) x
≥
4, x
≤
6 (c) x < 2, x
≥
-3
25.
Illustrate the following compound statements on a number line: (a)
-
1
≤
x
<
4
(b)
-
2
<
x
<
0
(c)
3
≤
x
<
7
(d)
-
5
<
x
<
5
(e)
-
5
≤
x
≤
3
26.
Illustrate the following compound statements on a number line: (a)
-
2
<
x
<
2
(b)
-
4
<
x
≤
-
1
(c)
-
9
≤
x
≤
15
(d)
0
≤
x
≤
10
(e)
4
>
x
≥
1
27.
Illustrate the following compound statements on a number line: (a)
1
5
<
x
<
1
3
(b)
2
1
2
≤
x
≤
3
1
5
(c)
-
0.75
<
x
≤
0.75
(d)
-
15
≤
x
≤
-
3
(e)
-
1
2
≤
x
≤
5
1
2
28.
Solve each of the following inequalities and represent your solution on a number line. (a) 2x + 4 > 10 (b) 3x – 5 < 2 (c) 5x +3 > 4 (d)
3
x
–
4
≤
-
13
(e)
3
x
-
7
≥
5
(f)
1
-
4
x
≥
9
29.
Solve each of the following inequalities and represent your solution on a number line. (a)
1
3
-
2
x
≤
-
8
1
3
(b)
3
(
1
–
x
)
+
4
(
x
+
3
)
≥
30
(c)
2
x
+
3
<
-
1
(d)
-
3
x
–
4
≤
2
(e)
-
4
-
2
3
x
≤
0
(f)
x
-
7
-
49
≤
-
1
7
30.
Solve each of the following simultaneous inequalities and illustrate your answers on a number line: (a)
x
+
3
>
5
x
-
4
<
4
(b)
x
+
10
≥
6
x
-
2
≤
3
(c)
-
5
x
+
7
<
12
1
3
x
+
2
≤
5
(d)
-
7
x
-
1
<
6
-
x
3
+
1
<
4
3
(e)
3
x
-
1
2
>
4
x
-
1
5
<
2
5
x
+
1
31.
Solve each of the following simultaneous inequalities and illustrate your answers on a number line: (a)
x
5
+
1
3
<
1
x
-
4
5
>
1
8
x
(b)
5
≤
3
x
+
2
3
x
–
14
<
-
2
(c)
x
3
+
2
3
<
2
-
1
2
x
+
1
<
2
(d)
x
+
2
2
<
5
-
x
+
6
3
<
4
(e)
9
–
2
x
≤
3
1
<
16
–
x
32.
Solve each of the following simultaneous inequalities and illustrate your answers on a number line: (a)
1
2
-
1
4
x
≤
x
=
2
(b)
12
–
x
≥
5
≤
2
x
–
2
(c)
-
4
x
<
6
≤
8
x
(d)
3
x
-
2
≥
-
4
≤
-
1
-
2
x
(e)
6
x
-
13
≤
17
<
8
x
-
7
(f)
2
x
+
3
>
5
x
-
3
>
-
8
33.
Show the regions that satisfy each of the following inequalities. (a)
x
≤
4
(b)
x
<
-
1
(c)
y
≥
-
4
(d)
y
+
2
<
-
5
(e)
3
-
x
>
7
(f)
y
-
1
4
≥
5
34.
Show the regions that satisfy each of the following inequalities. (a)
-
2
≤
1
2
x
<
7
(b)
-
≤
3
x
-
1
<
5
(c)
1
3
-
1
5
x
<
1
2
x
+
1
(d)
-
2
≤
x
<
7
(e)
1
2
x
+
1
2
>
1
4
(f)
1
7
x
-
1
3
<
1
5
+
x
3
35.
Show the regions that satisfy each of the following inequalities. (a)
x
>
-
7
(b)
y
≤
3
(c)
y
≤
0
(d)
x
+
2
≥
-
1
(e)
x
+
1
3
<
6
(f)
y
+
3
5
≤
2
36.
Show the regions that satisfy each of the following inequalities. (a)
-
4
<
y
≤
3
(b)
4
<
y
<
6
(c)
x
-
3
4
>
x
+
5
2
(d)
2
3
x
-
7
+
1
5
x
≥
-
x
3
(e)
x
2
-
4
x
≥
x
(
x
-
1
)
-
18
(f)
x
-
2
≥
4
+
3
x
37.
Graph each of the following inequalities: (a)
2
x
+
y
>
3
(b)
x
-
y
<
4
38.
Graph each of the following inequalities: (a)
3
x
+
2
y
>
12
(b)
3
y
+
x
≤
-
5
39.
Graph each of the following inequalities: (a)
y
+
4
x
<
3
(b)
y
-
1
2
x
≥
1
40.
Graph each of the following inequalities: (a)
2
x
>
y
+
4
(b)
1
5
x
+
1
3
y
≤
1
4
41.
Graph each of the following inequalities: (a)
2
y
-
3
x
-
5
≤
0
(b)
1
6
x
+
1
3
y
≤
-
1
42.
Graph each of the following inequalities: (a)
2
y
-
5
x
≥
7
(b)
1
2
x
-
y
≥
1
43.
Graph each of the following inequalities: (a)
3
(
1
2
x
-
1
y
y
)
≤
-
1
(b)
3
y
-
8
≥
-
6
x
44.
Graph each of the following inequalities: (a)
0.5
x
+
0.3
y
>
-
1
(b)
2
y
≥
0.75
-
x
45.
Graph the following inequality:
1
<
x
+
y
<
8
46.
Determine the inequalities which satisfy the following unshaded regions:
47.
Determine the inequalities which satisfy the following unshaded regions below:
48.
Determine the inequalities which satisfy the following unshaded regions drawn below:
49.
Draw the regions which satisfy the inequalities.
2
x
+
y
≥
6
x
<
3
y
<
6
50.
Draw the regions which satisfy the inequalities.
4
x
-
3
y
≤
12
x
>
0
y
>
0
51.
Draw the regions which satisfy the inequalities.
4
x
-
3
y
<
12
y
≥
0
y
≥
6
52.
Draw the regions which satisfy the inequalities.
y
+
2
x
≤
5
y
<
4
x
+
12
53.
Draw the regions which satisfy the inequalities.
y
-
x
<
0
x
≤
5
y
≥
0
54.
Draw the regions which satisfy the inequalities and hence write down the co-ordinates of any four points with integral values which lie in the region obtained.
2
x
+
y
>
4
6
x
+
2
y
≤
12
55.
Draw the regions which satisfy the inequalities.
x
+
y
≤
6
y
>
4
x
+
3
>
0
56.
Draw the regions which satisfy the inequalities and hence find the area of the required region.
5
x
+
3
y
≥
15
6
y
+
5
x
≤
30
y
≥
0
57.
Draw the regions which satisfy the inequalities and hence find the area of the required region.
0
≤
y
<
3
0
≤
x
<
4
58.
The vertices of the unshaded triangular region in the figure below are 0(0,0), A (8, 0) and B (8, 8). Write down the inequalities which are satisfied by the region.
59.
The figure below shows a square ABCD with vertices A (5, 0), B(0,5) C(-5, 0) and D. (a) Determine the co-ordinates of point D. (b) Write down the equations of lines AB, CB, CD and AD. (c) Write down the inequalities which determine the square.
60.
The figure below shows the vertices of a region bounded by lines AB, BC, CD and DA. Write down the inequalities that determine the region ABCD.
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