How do you solve compound Inequality #2/5x<6# and # -1/2x <= -10#?

Question

2258 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-08T12:50:20

No solution

At first we will solve

#2/5x<6#
multiplying by #5/2#
we get
#x<30/2=15#
No we solve the second inequality

#-1/2x<=-10#
multiplying by #-2#

#x>=20# (#<=# must be reversed to #>=#)
putting Things to gether

#20<=x<15#
which is impossible.

Answer 2 · 2018-07-08T12:52:10

No solution satisfies the conditions.

The first inequality is:

#2/5x<6#

Multiplying both sides by #5/2# yields:

#x<6*5/2#

#x<15#

The second inequality is:

#-1/2x<=-10#

Multiplying both sides by #-2# yields:

#x>=-10*-2#

#x>=20#

Since both inequalities of #x# cannot exist at the same time, we say the solution is #x<15# or #x>=20#.

But since the question asks for #bb(and)# and not #bb(or)#, we say that there is no solution that satisfies the given conditions.