How do you solve # -x / 7 + 4 ≥ 3x#?

2 Answers
Jun 19, 2018

Answer:

#x <= 14/11 " or " x <= 1 3/11#

Explanation:

Given: #-x/7 + 4 >= 3x#

The easiest way to start is to get rid of the fraction by multiplying the whole inequality by #7#:

#-x/cancel(7) *cancel(7)/1+ 4*7 >= 3x*7#

#-x+ 28 >= 21x#

Add #x# to both sides: #" "28 >= 22x#

Divide by #22#: #" "28/22 >= x#

Reduce the fraction: #" "14/11 >= x#

This means #x <= 14/11 " or " x <= 1 3/11#

Jun 19, 2018

Answer:

#x<=14/11#

Explanation:

To get rid of the #7# in the denominator, we can multiply all terms by #7#. This leaves us with

#-x+28>=21x#

Since we did the same thing to both sides, we did not inadvertently change the meaning of this equation.

What we can do next is add #x# to both sides. We get

#22x<=28#

Dividing both sides by #22# gives us

#x<=28/22#

which can be simplified as

#x<=14/11#

Hope this helps!