Question

Solve for x −ax + 2b > 8

Answer 1

Answer:
`x<(-8+2b)/(a)`

`a>0`

Explanation:

`-ax+2b>8`

`\mathrm{Subtract\:}2b\mathrm{\:from\:both\:sides}`

`-ax>8-2b`

`\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}`

`\left(-ax\right)\left(-1\right)<8\left(-1\right)-2b\left(-1\right)`

`ax<-8+2b`

`\mathrm{Divide\:both\:sides\:by\:}a`

`(ax)/(a)<-(8)/(a)+(2b)/(a);\quad \:a>0`

`x<(-8+2b)/(a);\quad \:a>0`

Answer 2

x < -( 8-2b) /a a > 0

Explanation:

−ax + 2b > 8

Subtract 2b from each side

−ax + 2b-2b > 8-2b

-ax > 8 -2b

Divide each side by -a, remembering to flip the inequality ( assuming a>0)

-ax/-a < ( 8-2b) /-a

x < -( 8-2b) /a a > 0