If x and y are negative numbers, is x<y?
Bunuel, can you please explain the graphical method to solve this question?
I'm happy to help with this. Idea #1
: to graph an inequality, solve for slope-intercept form
(i.e. y = mx + b form). When we do that
Graph (1) becomes: y > 3x/2 + 1/2
Graph (2) becomes: y > 2x/3 + 1/3
We plot the exact lines (y = 3x/2 + 1/2 and y = 2x/3 + 1/3) to determine the boundaries of the regions. If the inequality is y >
mx + b, then the region representing the inequality is above
the line; if the inequality is y <
mx + b, then the region representing the inequality is below
the line. Idea #2
: any question about whether x is > or = or < y is question about the line y = x. Read this post about the magical properties of the line y = x. http://magoosh.com/gmat/2012/gmat-math- ... -line-y-x/
Here's the image:
inequalities with y = x.JPG [ 82.84 KiB | Viewed 2391 times ]
The darker green region, above the line y > 3x/2 + 1/23, is the region representing the first inequality. The yellow region, above the line y = 2x/3 + 1/3, is the region representing the second inequality. The bright spring green region is their overlap, the region satisfied by both inequalities. Notice that everything in that bright spring green region is above the solid green line, which is y = x. Points above the line y = x always have y > x.
Does all this make sense?
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