# Linear Inequalities Questions and Answers - Form 2 Topical Mathematics

## Questions

1. Find without using a calculator, the value of:

2. Solve and write down all the integral values satisfying the inequality.
X – 9 ≤ - 4 < 3x – 4
3. Solve the inequality and show the solution on the number line.
3 – 2x <x <2x + 5
4. Show on a number line the range of all integral values of x which satisfy the following pair of inequalities
3 – x  ≤ 1 – ½ x
-½ (x-5) ≤ 7-x
5. Solve the inequalities 4x – 3 ≤6x – 1 <3x + 8; hence represent your solution on a number line
6. Find all the integral values of x which satisfy the inequalities
2(2-x)< 4x -9 < x + 11
7. Find the inequalities that define the unshaded region

8. Given that x + y = 8 and x²+ y²=34
Find the value of:-
1. x²+2xy+y²
2. 2xy
9. Find the inequalities satisfied by the region labelled R

10. The region R is defined by x ≥0, y ≥-2, 2y + x ≤2. By drawing suitable straight line on a sketch, show and label the region R
11. Find all the integral values of x which satisfy the inequality
3(1+ x) < 5x – 11 < x + 45
12. The vertices of the unshaded region in the figure below are O(0, 0) , B(8, 8) and A (8, 0). Write down the inequalities which satisfy the unshaded region

1. 12 x 0.25 – 12.4 ÷ 0.4 x 3
⅛ of 2.56 + 8.68
3 – 31 x 3
0.32 + 8.68
-90/9
= -10
2. x - 9 ≤- 4 <3x – 4
x – 9 ≤
- 4
x ≤
5
3x – 4 >
- 4
3x >
0
x = 0
0 >
x ≤5
{1, 2, 3, 4, 5}
3. x > 3 – 2x
x ≤
2x + 5/3
3 – 2x < x
-2x < x – 3

-3x < - 3
x < 1
2x + 5 ≥
3x
-x
5
x ≤
-5
-5 ≤
x < 1

4. 3 - x≤ 1 – ½x
3 – 1 ≤
x – ½x
2≤ ½ x
x
4
-x + 5≤ 14 – 2x
2x – x ≤ 14 – 5
x≤ 9
4
≤ X ≤ 9

5. 4x – 3 ≤6x – 1
-2x ≤
2
x ≥
-1
6x – 1 <
3x + 8
3x <
9
x <
3
-1 ≤
x <3

6. 2(2-x ) <4x -9
4 – 2n <
4x -9
4 + 9 <
4x + 2n = 13 6x
=
13/6 n = 21/6 < n
and 4x – 9 <
x + 11
4n –n < 11 + 9
3n < 20
x <
20/3= < 2/3
Integral values 3, 4, 5, 6
7. L3 : y ≥ 1
L
1: y + x ≥ - 1
L
2: y – x
1. x2 + 2xy + y2 = x2 + xy + xy + y2
= x(x + y) + y(x + y)
= (x + y) (x + y)
∴ (x + y)2 = 8 x 8 = 64
2. x2 + 2xy + y2 = 64
(x
2 + y2) + 2xy = 64
34 + 2xy = 64
2xy = 30
8. Equation of L1
(3.5, 4) (0, 2)
y-2  2
x-0    3.5-0
3.5y – 7 = 2x
∴y =4/7x = 2x
Inequality of
y ≤
4/7x + 2
Or
7y ≤ 4x + 14
Equation of L2
(0, 3) (4, 2)
y - 2 3- 2
x – 4     0 -4
-4(y-2) = x-4
-4y + 8 = x -4
-4y = x -12
inequality y ≥
- ¼ x + 3
4y ≥
–x + 12
Equation of L3
y - 2  2
x – 4   -0.5
-0.5(y-2) = 2(x-4)
-5y + 1 = 2x -8
-5y = 2x - 9
y = -4x + 18
in equality y ≤
-4 x+ 18
9. Lines to be drawn x = 0, y = 2
2y + x = 2
 x 0 2 y 1 0
10. 3(1 + x) < 5x – 11
3 +3 x) < 5x – 11
-2x < - 14
x >7
5x – 11< 45
5x < 56
x < 11.2
Integral values are 8, 9, 10, 11
11. y ≤ x
x ≤ 8
y ≤ 0

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