Question

2/3x+14-3x>-7

i’m not that good when it comes to fractions so i just need some help to understand it easier.

Answer 1

x < 9

Explanation:

`(2)/(3) x+14-3x>-7`

First, write 3 as a fraction:

`(2)/(3) x+14-(3)/(1)x>-7`

The common denominator is 3, so:

`(2)/(3) x+14-(9)/(3)x>-7`

Combine the fractions:

`(2-9)/(3) x+14>-7\\-(7)/(3) x+14>-7`

Subtract 14 from both sides:

`-(7)/(3) x>-21`

Multiply both sides by 3:

`-7x>-63`

Divide both sides by -7 (don't forget to flip the sign when multiplying or dividing by a negative number):

`x<9`

Answer 2

`\large\boxed{x<9\to x\in(-\infty,\ 9)}`

Explanation:

`(2)/(3)x+14-3x>-7\qquad\text{subtract 14 from both sides}\\\\(2)/(3)x+14-14-3x>-7-14\\\\(2)/(3)x-3x>-21\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot(2)/(3\!\!\!\!\diagup_1)x-(3)(3x)>(3)(-21)\\\\2x-9x>-63\\\\-7x>-63\qquad\text{change the signs}\\\\7x<63\qquad\text{divide both sides by 7}\\\\(7x)/(7)<(63)/(7)\\\\x<9`