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JSS2: MATHEMATICS - 3RD TERM

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  1. Expansion and Factorization of Algebraic Expressions | Week 1
    4Topics
    |
    1 Quiz
  2. Algebraic Expansion and Factorization of Algebraic Expression | Week 2
    4Topics
    |
    1 Quiz
  3. Algebraic Fractions I | Week 3
    4Topics
    |
    1 Quiz
  4. Addition and Subtraction of Algebraic Fractions | Week 4
    2Topics
    |
    1 Quiz
  5. Solving Simple Equations | Week 5
    4Topics
    |
    1 Quiz
  6. Linear Inequalities I | Week 6
    4Topics
    |
    1 Quiz
  7. Linear Inequalities II | Week 7
    2Topics
    |
    1 Quiz
  8. Transactions in the Homes and Offices | Week 8
    5Topics
    |
    1 Quiz
  9. Quadrilaterals | Week 9
    2Topics
    |
    1 Quiz
  10. Angles in a Polygon | Week 10
Lesson 6, Topic 3
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Graphs of Linear Inequalities

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Inequalities are said to be linear, if they have no square or higher powers of the unknown. In other words, the highest power of the unknown is 1.

E.g

\( \scriptsize 2x > 10 \)

\( \scriptsize 4x \: – \: 5y > \: -18 \)

Number Line

A number line is a visual representation of the set of real numbers as a series of points.

number line

Showing Inequalities on a Number Line 

On a number line, you can show inequality by obeying these rules. 

For ‘<’ the arrow points to the left, but the starting point is not shaded 

For Example, x < 5 is drawn this way

x5 e1622630513338

For ‘>’, the arrow points to the right direction and the starting point is not shaded.

E.g. x > 5 is drawn this way 

x5 1 e1622631385863

3. For \( \scriptsize ‘ \leq ‘ \) , the arrow points to the left and the starting point is shaded.

e.g \( \scriptsize x \leq \: -2 \), is drawn this way. 

x leq 2 e1622632001329

3. For \( \scriptsize ‘ \geq ‘ \) , the arrow points to the left and the starting point is shaded.

e.g \( \scriptsize x \geq \: -2 \), is drawn this way. 

x 2 e1622632281581

Example 1 

Show the following inequalities on a number line

(a) \( \scriptsize x > 3 \)

(b) \( \scriptsize x \leq 3 \)

(c) \( \scriptsize x \geq 3 \)

Solution

(a) \( \scriptsize x > 3 \)

g 3 e1622633428800

(b) \( \scriptsize x \leq 3 \)

number line3 e1622632903432

(c) \( \scriptsize x \geq 3 \)

geq 3 e1622633491850

Example 2

Show each of these inequalities on a number line 

(a) \( \scriptsize x < 4 \)

(b) \( \scriptsize x > 4 \)

(c) \( \scriptsize x \leq 4 \)

(d) \( \scriptsize x \geq 4 \)

Solution

(a) \( \scriptsize x < 4 \)

l4 e1622635127728

(b) \( \scriptsize x > 4 \)

g4 e1622635329479

(c) \( \scriptsize x \leq 4 \)

leq 4 e1622635442491

(d) \( \scriptsize x \geq 4 \)

geq 4 e1622635507884

Example 3

Use suitable symbols to write the inequalities shown in the following number line

(a)

x geq 3 e1622636002716

(b)

x leq 2 1 e1622636217482

(c)

x geq 1 e1622636120640

(d)

x 5 e1622636277310

Answers

(a) \( \scriptsize x \geq -3 \)

(b) \( \scriptsize x \leq 2 \)

(c) \( \scriptsize x \geq -1 \)

(d) \( \scriptsize x < 5 \)

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