Question

Help me answer all of them ;-;

Answer 1

2) D, 3) A, 4) A, 5) B

Explanation:

2) We proceed to demonstrate the statement algebraically:

(i)
`3\cdot (m+2)-4\cdot (2\cdot m -9)` Given.

(ii)
`3\cdot m + 6 + (-4)\cdot (2\cdot m) +(-4)\cdot (-9)` Distributive property.

(iii)
`3\cdot m +6 +[(-4)\cdot (2)]\cdot m + (-4)\cdot (-9)` Associative property.

(iv)
`3\cdot m + 6 -8\cdot m + 36`
`(-a)\cdot b = -a\cdot b`/
`(-a)\cdot (-b) = a\cdot b`

(v)
`-5\cdot m +42` Distributive property/Definition of addition/Result.

Answer: D

3) We proceed to demonstrate the statement algebraically:

(i)
`-2\cdot (4\cdot x -5\cdot y - 5\cdot x )` Given.

(ii)
`-2\cdot [(4-5)\cdot x - 5\cdot y]` Associative and distributive properties.

(iii)
`-2\cdot (-x-5\cdot y)` Definition of addition.

(iv)
`(-2)\cdot (-x) + [(-2)\cdot (-5)]\cdot y` Distributive and associative properties.

(v)
`2\cdot x + 10\cdot y`
`(-a)\cdot (-b) = a\cdot b`/Result

Answer: A

4) We proceed to demonstrate the statement algebraically:

(i)
`-(8)/(9)\cdot \left(27+(2)/(3)\cdot x \right)` Given.

(ii)
`\left(-(8)/(9) \right)\cdot (27) + \left[\left(-(8)/(9) \right)\cdot \left((2)/(3) \right)\right]\cdot x` Distributive property.

(iii)
`-24-(16)/(27)\cdot x`
`(a)/(b)\cdot c = (a\cdot c)/(b)`/
`(-a)\cdot b = -a\cdot b`/Associative property/
`(a)/(b)\cdot (c)/(d) = (a\cdot c)/(b\cdot d)`/
`(a\cdot c)/(b\cdot c) = (a)/(b)`/Result

Answer: A

5) We proceed to demonstrate the statement algebraically:

(i)
`-(1)/(3)\cdot \left(3\cdot x -(1)/(2) \right)` Given.

(ii)
`\left[\left(-(1)/(3) \right)\cdot 3\right]\cdot x +\left(-(1)/(3) \right)\cdot \left(-(1)/(2) \right)` Distributive property.

(iii)
`-x +(1)/(6)`
`(-a)\cdot b = -a\cdot b`/
`(-a)\cdot (-b) = a\cdot b`/
`(a)/(b)\cdot (c)/(d) = (a\cdot c)/(b\cdot d)`/
`(a\cdot c)/(b\cdot c) = (a)/(b)`/Result

Answer: B