Question

Solve for X:

kx−y ≥ x+z
if k is greater then 1, what is x
if k is less then 1, what is x
is k is equal to 1, then what is x

Answer 1

kx-y≥x+z

minus x both sides
kx-x-y≥z
add y to both sides
kx-x≥y+z
undistribute x
x(k-1)≥y+z
divide both sides by (k-1)

`x= (y+z)/(k-1)`

if k is greater than 1, then the denomenator is positive, then x is positive (assuming z+y is positive)

if k is les than 1, the the denomenator is negatve, then x is negative

if k is equal to 1, then x is undefined

Answer 2

k greater than 1

(k-1)x>z
x>z/(k-1)

k less than 1

-z-y/(1-k)>x

k equal to 1

0>y+z