Solve for #x#? #3(x-4)<12 or 4(x+3)<12#

1 Answer

Answer:

#x<8#

Explanation:

We have two inequalities that are linked with an "or", which means that so long as we have a valid #x# for one of the equations, it'll be part of the solution set (whereas if we had "and", we'd need the #x# values to be valid in both equations).

Let's solve them individually and see what we get:

Equation 1

#3(x-4)<12#

#x-4<4#

#x<8#

Equation 2

#4(x+3)<12#

#x+3<3#

#x<0#

Putting it together

We have #x<8# or #x<0#. Again, so long as we have a valid #x# value in one inequality, it's part of the solution.

#" OR "# means either of the conditions must be true.

#x<8#, since it includes all the solutions in #x<0# and more, is the final answer.

However, if it had been #x<0 " AND " x <8#, then BOTH conditions have to be true and the solution would be #x<0#