Question

What are some possible solutions for the following inequality?

-3x+5x-2>-4x+1

Answer 1

Any value greater than 0.5.

Explanation:

First, set the inequality to an equation and solve for x:

`-3x+5x-2=-4x+1\\2x-2=-4x+1\\2x-2+4x=-4x+1+4x\\6x-2=1\\6x-2+2=1+2\\6x=3\\((1)/(6))6x=3((1)/(6))\\x=(1)/(2)`

This is the value at which the inequality equals 0. To test the inequality and determine whether x is greater or less than
`(1)/(2)`, choose any value of x that is easy to work with on either side of
`(1)/(2)`:

For x=0:

-3(0)+5(0)>-4(0)+1

0>1 This is not a true statement. Therefore, x is not less than
`(1)/(2)`.

For x=1:

-3(1)+5(1)>-4(1)+1

-3+5>-4+1

2>-3 This is a true statement. Therefore, x is any value greater than
`(1)/(2)`.

Answer 2

x>1/2 is a solution