Question #070dd

2 Answers
Apr 21, 2017

#2(x+8)\ge -36# or #x \ge -26#


"Twice" = #2 \times(stuff)#
"The sum of x and 8" = #x+8#

So "twice the sum of x and 8" = 2(x+8)

And "twice the sum of x and 8 is greater than or equal to -36" means:

#2(x+8)\ge -36#
This is the translation of the above statement into an inequality.

If you want to solve this, first divide by 2

#x+8\ge -18#

then subtract 8, to get:

#x \ge -26#

Apr 21, 2017

#2*(x + 8) >= -36#


This is a good example of how mathematical expressions can more succinctly describe relationships than other languages! The write it our (translate it, if you will) we need to ‘convert’ the words to math symbols.

Twice something is “2 times”, or “2 * (expression)”.
A sum is the addition of the two (or more) items: x + 8
Greater than is a larger value, indicated by the > sign, and equal to is the “=” sign. Combined, we write them as #>=#.

Putting these together, we have:
#2*(x + 8) >= -36#

The “inequality” is just that it is NOT a single value “equal” to something, but a whole range of values that are more or less than the ‘index’ value.