Inequality with negative constants

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SUMMARY

The discussion focuses on solving the inequality ax + b < c, where a, b, and c are negative constants. The solution process involves rearranging the inequality to isolate x, resulting in x > (c - b) / a. Since a is negative, dividing by a reverses the inequality, leading to the conclusion that x must be greater than (c - b) / a. The participants suggest rewriting the constants as positive values (A = -a, B = -b, C = -c) for clarity in solving the inequality.

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Homework Statement



Solve each of the following inequalities; give your answers in interval notation.

i) ax + b < c, where a, b, c are negative constants


Homework Equations





The Attempt at a Solution





ax < c - b
x > c - b / a
because I'm dividing by a negative constant.

x > -b + c / a
 
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try rewriting the equation using
A = -a
B = -b
C = -c

then A,B,C are all positive & things shoud be a little clearer
 

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