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Q1: Represent [tex][tex]$\sqrt{8}$[/tex][/tex], [tex][tex]$\frac{7}{8}$[/tex][/tex], and [tex][tex]$\sqrt{2}$[/tex][/tex] on the number line.

Q2: Identify the property that justifies each of the following statements:

i) [tex]-x + 9 = 9 + x[/tex]

ii) [tex]2(x + 3) = 2x + 6[/tex]

iii) [tex](5y) \times 1 = 5y[/tex]

iv) If [tex]8 + 2 \ \textless \ 14 \ \textless \ 20[/tex], then [tex]8 + 2 \ \textless \ 20[/tex]

v) If [tex](m - n) \ \textless \ (p + q)[/tex] and [tex]r \ \textgreater \ 0[/tex], then [tex](m - n)r \ \textless \ (p + q)r[/tex]

vi) If [tex]q + r = 15[/tex], then [tex]15 = q + r[/tex]



Answer :

GinnyAnswer
Let's address both questions in detail:

### Q1 - Represent √8, 7/8, and √2 on the number line

#### √8 on the Number Line:
1. Approximate the value: √8 is approximately equal to 2.828.
2. Mark points 0, 1, 2, 3 on the number line.
3. Place √8 between 2 and 3, closer to 3 (since 2.828 is closer to 3).

#### 7/8 on the Number Line:
1. Approximate the value: 7/8 is equal to 0.875.
2. Mark points 0 and 1 on the number line.
3. Divide the segment between 0 and 1 into eight equal parts.
4. Identify the 7th division on this segment. This point represents 7/8.

#### √2 on the Number Line:
1. Approximate the value: √2 is approximately equal to 1.414.
2. Mark points 0, 1, and 2 on the number line.
3. Place √2 between 1 and 2, closer to 1 (since 1.414 is between 1 and 2).

### Q2 - Identify the property that justifies each equation or inequality:
- i) -x + 9 = 9 + x:
- This represents the Commutative Property of Addition. This property states that the order in which numbers are added does not affect the sum.

- ii) 2(x + 3) = 2x + 6:
- This represents the Distributive Property. The distributive property states that a(b + c) = ab + ac.

- iii) (5y) * 1 = 5y:
- This represents the Multiplicative Identity Property. This property states that any number multiplied by 1 remains the same.

- iv) If 8 + 2 < 14 < 20, then 8 + 2 < 20:
- This represents the Transitive Property of Inequality. This property states that if a < b and b < c, then a < c.

- v) If (m - n) < (p + q) and r > 0, then (m - n)r < (p + q)r:
- This represents the Multiplication Property of Inequality. If a < b and c > 0, then ac < bc.

- vi) If q + r = 15, then 15 = q + r:
- This represents the Symmetric Property of Equality. This property states that if a = b, then b = a.

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