Question

Which of the following is the solution to the inequality below?
-3/2(x-1/3)>1/5-5x

Answer 1

For this case we have the following inequality:

`- \frac {3} {2} (x- \frac {1} {3})> \frac {1} {5} -5x`

We apply distributive property on the left side:

`- \frac {3} {2} x + \frac {3} {6}> \frac {1} {5} -5x`

We add 5x to both sides:

`5x- \frac {3} {2} x + \frac {3} {6}> \frac {1} {5}\\\frac {7} {2} x + \frac {3} {6}> \frac {1} {5}`

We subtract
`\frac {3} {6}` on both sides:

`\frac {7} {2} x> \frac {1} {5} - \frac {3} {6}\\\frac {7} {2} x> - \frac {9} {30}\\7x> - \frac {18} {30}\\7x> - \frac {3} {5}`

We divide between 7 on both sides:

`x> - \frac {3} {35}`

Answer:

`x> - \frac {3} {35}`