I hope this isn't too vague of a question. I'm currently stuck on how to approach khan Academy's "Analyzing structure with linear inequalities" problems. I remember doing these problems before, enough to get the "mastered" mark on khan academy but I was so stuck on these types of problems that I eventually started getting the same questions and clicking on the correct answers.
Sal Khan did walk me through some of the problems but I fail to see what his strategy is other than guess and check. Is that what I'm supposed to be doing? The full problem can't fit in one image. Sorry!
You do not need to guess. You need to:
1) translate each statement from words to an inequality
2) perform substitutions, or use intermediate expressions, to get an inequality comparing the two expressions that you’re asked to compare.
In example 1, we’re told: $a>b$, $b>c$, and $a>b+c$.
Then we’re asked to compare $b+c$ with $2a-b$.
Using what we’re told: $2a-b = a+a-b > (b+c)+(b+c)-b=b+2c>b+c$
In the second example, we’re told:
$b>8$, and $p>2(b+8)$
Then we’re asked to compare $p$ and 30.
So using what we were told:
$p > 2(b+8) > 2(8+8) = 32 > 30$