How do you solve #\frac { - 5x } { 4} \geq 2\cdot ( \frac { x } { 2} + 3)#?

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Answer 1 · 2017-06-05T03:36:20

#x<=-8/3#

See the process below.

Solve:

#(-5x)/4>=2*(x/2+3)#

Expand the right side.

#(-5x)/4>=(2x)/2+6#

Simplify.

#(-5x)/4>=cancel((2)x)/cancel2#

#(-5x)/4>=x+6#

Multiply both sides by #4#.

#-5x>=4(x+6)#

Expand.

#-5x>=4x+24#

Subtract #4x# from both sides.

#-5x-4x>=24#

Simplify.
#-9x>=24#

Multiply both sides by #-1#. This will make the left side positive and reverse the inequality.

#9x<=-24#

Divide both sides by #9#.

#x<=-24/9#

Divide the numerator and denominator by #3#.

#x<=-(24÷3)/(9÷3)#

Simplify.

#x<=-8/3#