Question

Please help me! I'm stuck and really confused, thank you so much!

Answer 1

(a)
`5 * (2x - 1) = 10x - 5`

(b)
`6 * x = x + 2x + 3x`

(c)
`(1)/(2)(x - 6) = (1)/(2)x - 3`

(d)
`y(3x + 4z) = 3xy + 4yz`

(e)
`z(2xy - 3y + 4x) = 2xyz - 3yz + 4xz`

Explanation:

Solving (a):

Given

`10x - 5`

Required

Express as a product

Express 10x as 5 * 2x

`10x - 5 = 5 * 2x - 5`

Apply distributive property

`10x - 5 = 5(2x - 1)`

`10x - 5 = 5 * (2x - 1)`

So:

`5 * (2x - 1) = 10x - 5`

Solving (b):

Given

`x + 2x + 3x`

Required

Express as a product

Express 2x and 3x as 2 * x and 3 * x, respectively

`x + 2x + 3x = x + 2*x + 3*x`

Apply distributive property

`x + 2x + 3x = x(1 + 2 + 3)`

`x + 2x + 3x = x(6)`

`x + 2x + 3x = 6*x`

So:

`6 * x = x + 2x + 3x`

Solving (c):

Given

`(1)/(2)(x - 6)`

Required

Express as a sum/difference

Apply distributive property

`(1)/(2)(x - 6) = (1)/(2)x - (1)/(2)*6`

`(1)/(2)(x - 6) = (1)/(2)x - (6)/(2)`

`(1)/(2)(x - 6) = (1)/(2)x - 3`

Solving (d):

Given

`y(3x + 4z)`

Required

Express as a sum/difference

Apply distributive property

`y(3x + 4z) = 3x * y + 4z * y`

`y(3x + 4z) = 3xy + 4yz`

Solving (e):

Given

`2xyz - 3yz + 4xz`

Required

Express as a product

Factorize

`2xyz - 3yz + 4xz = 2xy * z - 3y * z + 4x * z`

Apply distributive property

`2xyz - 3yz + 4xz = z(2xy - 3y + 4x)`

So:

`z(2xy - 3y + 4x) = 2xyz - 3yz + 4xz`