How do you solve #2p - ( 3- p ) \leq - 7p - 2#?

Question

Abigail Allen · Accepted Answer

#p <= 1/10#

Given: #2p - (3 - p) <= - 7p -2#

We need to get rid of the brackets and since there is a #-# sign in front of the brackets, everything inside changes its sign:

#2p - 3 + p <= - 7p -2#

Then we can sort out all the terms to move the unknowns from the numbers; be very careful with the signs:

#2p - 3 + p <= - 7p -2# #2p + p +7p <= 3 -2# #10p <= 1#

#p <= 1/10#

That means if BIG #P# were a centimeter #(cm)# then our #p# would be #1/10 color(red) or# smaller than a millimeter #(mm)#.

To make sure the answer is correct, put it back into the #given# equation. Now we are using the largest value that #p# can be, or the value at which #p color(red)=1/10#. We will then need to adjust the equation to reflect the following #equality#.

#2p - (3 - p) color(red) = - 7p -2#

#2(1/10) - (3 -1/10) color(red)= - 7 xx 1/10 -2#

#2/10 - 3 + 1/10 color(red)= - 7/10 -2#

#-2 - 7/10 color(red)= - 7/10 -2#

Note: because #p<=1/10# there are an infinite number of answers smaller than #p = 1/10# which when substituted into the #given# equation will all result in an inequality.

Examples: #p<=1/10# means:

#p=1/10; p=1/50; p=-1/100; p=-100# ....