Homework Help

can you solve -5x/7-2>-7 ?

user profile pic

gdblu | eNotes Newbie

Posted June 3, 2013 at 1:20 PM via web

dislike 2 like

can you solve -5x/7-2>-7 ?

1 Answer | Add Yours

user profile pic

mvcdc | Student, Undergraduate | (Level 1) Associate Educator

Posted June 3, 2013 at 1:35 PM (Answer #1)

dislike 2 like

We want so solve for x in the following inequality:

`-(5x)/7 - 2 > -7`

There are a lot of ways we can manipulate this (meaning, different possible ways of operating on the left hand side and the right hand side) to isolate x. I will do one here.

`-(5x)/7 - 2 + 2 > -7 + 2` (added 2 to both sides of the equation)

`-(5x)/7 > -5`

`-(5x)/7 * 7 > -5 * 7` (multipled 7 to both sides)

`-5x > -35`

`5x < 35` (got rid of the negative sign; reverse inequality)

`5x * 1/5 < 35 * 1/5` (divide both sides by 5 - same as multiplying by 1/5)

`x < 7`

 

*Of course you can multiply first (to get rid of the 7 in the denominator), and then proceed with the other manipulation as follows:

`-(5x)/7 - 2 > -7` 

`-5x - 14 > -49`

`-5x > -35`

`x < 7`

 

We solved this using the rules and properties involving inequalities (see link below).

Sources:

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes