Question

25. Name the property used in each step.

Given: 2(x + 3) – 4(x – 4)
= 2x + 6 – 4x + 16 ________________________________
= 2x – 4x + 6 + 16 ________________________________
= x(2 – 4) + 6 + 16 ________________________________
= x(-2) + 6 + 16 ________________________________
= -2x + 6 + 16 ________________________________
= -2x + 22 ________________________________

Answer 1

i) Given, ii) Distributive property, iii) Commutative property, iv) Distributive property, v) Substraction, vi) Law of signs, multiplication, vi) Sum. Result.

Explanation:

25) Name the property used in each step:

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

ii)
`2\cdot x + 6 - 4\cdot x + 16` Distributive property.

iii)
`2\cdot x - 4\cdot x + 6 +16` Commutative property.

iv)
`x \cdot (2 - 4) + 16 + 16` Distributive property.

v)
`x \cdot (-2) + 6 + 16` Substraction.

vi)
`-2\cdot x + 6 + 16` Law of signs, multiplication.

vii)
`-2\cdot x + 22` Sum. Result.