Answer:
2) D, 3) A, 4) A, 5) B
Step-by-step explanation:
2) We proceed to demonstrate the statement algebraically:
(i) [tex]3\cdot (m+2)-4\cdot (2\cdot m -9)[/tex] Given.
(ii) [tex]3\cdot m + 6 + (-4)\cdot (2\cdot m) +(-4)\cdot (-9)[/tex] Distributive property.
(iii) [tex]3\cdot m +6 +[(-4)\cdot (2)]\cdot m + (-4)\cdot (-9)[/tex] Associative property.
(iv) [tex]3\cdot m + 6 -8\cdot m + 36[/tex] [tex](-a)\cdot b = -a\cdot b[/tex]/[tex](-a)\cdot (-b) = a\cdot b[/tex]
(v) [tex]-5\cdot m +42[/tex] Distributive property/Definition of addition/Result.
Answer: D
3) We proceed to demonstrate the statement algebraically:
(i) [tex]-2\cdot (4\cdot x -5\cdot y - 5\cdot x )[/tex] Given.
(ii) [tex]-2\cdot [(4-5)\cdot x - 5\cdot y][/tex] Associative and distributive properties.
(iii) [tex]-2\cdot (-x-5\cdot y)[/tex] Definition of addition.
(iv) [tex](-2)\cdot (-x) + [(-2)\cdot (-5)]\cdot y[/tex] Distributive and associative properties.
(v) [tex]2\cdot x + 10\cdot y[/tex] [tex](-a)\cdot (-b) = a\cdot b[/tex]/Result
Answer: A
4) We proceed to demonstrate the statement algebraically:
(i) [tex]-\frac{8}{9}\cdot \left(27+\frac{2}{3}\cdot x \right)[/tex] Given.
(ii) [tex]\left(-\frac{8}{9} \right)\cdot (27) + \left[\left(-\frac{8}{9} \right)\cdot \left(\frac{2}{3} \right)\right]\cdot x[/tex] Distributive property.
(iii) [tex]-24-\frac{16}{27}\cdot x[/tex] [tex]\frac{a}{b}\cdot c = \frac{a\cdot c}{b}[/tex]/[tex](-a)\cdot b = -a\cdot b[/tex]/Associative property/[tex]\frac{a}{b}\cdot \frac{c}{d} = \frac{a\cdot c}{b\cdot d}[/tex]/[tex]\frac{a\cdot c}{b\cdot c} = \frac{a}{b}[/tex]/Result
Answer: A
5) We proceed to demonstrate the statement algebraically:
(i) [tex]-\frac{1}{3}\cdot \left(3\cdot x -\frac{1}{2} \right)[/tex] Given.
(ii) [tex]\left[\left(-\frac{1}{3} \right)\cdot 3\right]\cdot x +\left(-\frac{1}{3} \right)\cdot \left(-\frac{1}{2} \right)[/tex] Distributive property.
(iii) [tex]-x +\frac{1}{6}[/tex] [tex](-a)\cdot b = -a\cdot b[/tex]/[tex](-a)\cdot (-b) = a\cdot b[/tex]/[tex]\frac{a}{b}\cdot \frac{c}{d} = \frac{a\cdot c}{b\cdot d}[/tex]/[tex]\frac{a\cdot c}{b\cdot c} = \frac{a}{b}[/tex]/Result
Answer: B
