Question

How do you evaluate `\frac { 3} { 8} x > 5`?

Answer 1

`x > 40/3`

Explanation:

`3/8x > 5`

Cross multiply

`(3x)/8 > 5/1`

`3x xx 1 > 5 xx 8`

`3x > 40`

Divide both sides by `3`

`(3x)/3 > 40/3`

`x > 40/3`

Answer 2

See a solution process below:

Explanation:

Multiply each side of the inequality by the reciprocal of the coefficient for `x` or, in other words, multiply by `color(red)(8)/color(blue)(3)` to solve for `x` while keeping the inequality balanced:

`color(red)(8)/color(blue)(3) xx 3/8x > color(red)(8)/color(blue)(3) xx 5`

`cancel(color(red)(8))/cancel(color(blue)(3)) xx color(blue)(cancel(color(black)(3)))/color(red)(cancel(color(black)(8)))x > 40/3`

`x > 40/3`