How do you write the inequality and solve given "two thirds of a number plus 5 is greater than 12"?

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Answer 1 · 2017-02-13T23:52:02

The inequality is: #2/3n + 5 > 12#

The solution is: #n > 21/2#

First, let's call the number we are going to solve for #n#.

Then two thirds of this number can be written as:

#2/3n#

Then if we "plus 5" or, in other words, add 5 we get:

#2/3n + 5#

Finally, if this is "greater than 12" we can finalize the inequality by writing:

#2/3n + 5 > 12#

Now, to solve this we first subtract #color(red)(5)# from each side of the inequality to isolate the #n# term while keeping the inequality balanced:

#2/3n + 5 - color(red)(5) > 12 - color(red)(5)#

#2/3n + 0 > 7#

#2/3n > 7#

Then, we multiply each side of the inequality by #color(red)(3)/color(blue)(2)# to solve for #n# while keeping the inequality balanced:

#color(red)(3)/color(blue)(2) xx 2/3n > color(red)(3)/color(blue)(2) xx 7#

#cancel(color(red)(3))/cancel(color(blue)(2)) xx color(blue)(cancel(color(black)(2)))/color(red)(cancel(color(black)(3)))n > 21/2#

#n > 21/2#