25 Algebraic Inequalities
By studying this lesson you will be able to
• solve inequalities and representing the solutions on a number line,
• represent inequalities on a coordinate plane.
Let us recall what has been learnt earlier about inequalities by considering the
following examples.
Example 1
Solve the inequality x + 20 > 50 and
(i) write down the set of integral values that x can take.
(ii) represent the integral values that x can take on a number line.
x + 20 > 50
x > 50 – 20
x > 30
(i) {31, 32, 33, 34, ....}
(ii)
28 29 30 31 32 33 34 35 36
Example 2
Solve the inequality and represent all the values that x can take on a
number line.
(When an inequality is divided by a
negative number, the inequality sign changes)
–8 –7 –6 –5 –4 –3 –2 –1 0 1
78 For free distribution
, Review Exercise
1. Solve each of the following inequalities.
2. Solve each of the following inequalities and represent the solutions on a number
line.
3. For each of the following inequalities, one of the values of x which satisfies the
inequality is given within the brackets. Select that value and underline it.
4. (i) Solve the inequality x + 1 > – 2 and write down the smallest integral value
that x can take.
(ii) Solve the inequality –3y > 15 and write the largest integral value that y can
take.
5. Solve the inequalities x + 3 > 1 and and represent all the solutions on
a number line.
25.1 Inequalities of the form
Example 1
Nimal who constructed a rectangular structure of breadth 5 cm as shown in the
figure using a 30 cm long piece of wire, saved a small piece of the wire.
x cm
5 cm
If the length of the rectangle is taken as x, an inequality in terms of x, involving the
perimeter of the rectangular structure is given by 2x + 10 < 30. On a number line,
For free distribution 79
By studying this lesson you will be able to
• solve inequalities and representing the solutions on a number line,
• represent inequalities on a coordinate plane.
Let us recall what has been learnt earlier about inequalities by considering the
following examples.
Example 1
Solve the inequality x + 20 > 50 and
(i) write down the set of integral values that x can take.
(ii) represent the integral values that x can take on a number line.
x + 20 > 50
x > 50 – 20
x > 30
(i) {31, 32, 33, 34, ....}
(ii)
28 29 30 31 32 33 34 35 36
Example 2
Solve the inequality and represent all the values that x can take on a
number line.
(When an inequality is divided by a
negative number, the inequality sign changes)
–8 –7 –6 –5 –4 –3 –2 –1 0 1
78 For free distribution
, Review Exercise
1. Solve each of the following inequalities.
2. Solve each of the following inequalities and represent the solutions on a number
line.
3. For each of the following inequalities, one of the values of x which satisfies the
inequality is given within the brackets. Select that value and underline it.
4. (i) Solve the inequality x + 1 > – 2 and write down the smallest integral value
that x can take.
(ii) Solve the inequality –3y > 15 and write the largest integral value that y can
take.
5. Solve the inequalities x + 3 > 1 and and represent all the solutions on
a number line.
25.1 Inequalities of the form
Example 1
Nimal who constructed a rectangular structure of breadth 5 cm as shown in the
figure using a 30 cm long piece of wire, saved a small piece of the wire.
x cm
5 cm
If the length of the rectangle is taken as x, an inequality in terms of x, involving the
perimeter of the rectangular structure is given by 2x + 10 < 30. On a number line,
For free distribution 79
