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About Paul Klarreich
Expertise
I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction.
I can also try (but not guarantee) to answer questions on Abstract Algebra
-- groups, rings, etc. and Analysis -- sequences, limits, continuity.
I won't understand specialized engineering or business jargon.
Experience
I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.
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You are here: Experts > Science > Mathematics > Advanced Math > Inequalities - graphing
Expert: Paul Klarreich
Date: 5/8/2008
Subject: Inequalities - graphing
Question
I need help solving the following problem:
Directions: Graph the inequality.
Problem: 9x is less than or equal to 7y
Already: I have already divided both sides by 7 and now have 9/7x is less than or equal to y.
What next!?
Answer
Questioner: Anna
Category: Advanced Math
Private: No
Subject: 6th grade Algebra 1 honors
Question: I need help solving the following problem:
Directions: Graph the inequality.
Problem: 9x is less than or equal to 7y
Already: I have already divided both sides by 7 and now have 9/7x is less than or equal to y.
What next!?
........................................
Hi, Anna,
How could you play that Ace of hearts? You could....
oops -- sorry, that's some other Anna.
About your question:
9x <= 7y.
This is a 2-dimensional equality. Your answer is going to be some area of the plane, which you will shade in.
Try putting the y on the left. It just 'reads' better.
7y >= 9x ::: see how the inequality switches, too.
y >= 9x/7 ::: or (9/7)x. But 9/7x is confusing.
Since y is up-down. "y >" means 'above.'
Ready to go to work:
TEMPORARILY: write
y = 9x/7 ::: equals, for now.
Graph this line. It goes through (0,0) and has slope 9/7.
Quick and dirty way: let x = 7, then y = 9 and plot (7,9).
Draw your line lightly through (0,0) and (7,9). Now
y >= 9x/7 means y is 'above and equal' to the line.
Draw the line REAL HEAVY AND SOLID now. Then shade the part of the paper above it.
Done.
(see attached picture.)
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