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Somewhat, but the rules are a bit different for inequalities. Example. -2X > 4 X < - 2 See, sign changes when dividing by negative coefficient.
A binomial coefficient is a coefficient of any of the terms in the expansion of the binomial (x+y)^n.
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In the form y=mx+b, b is the y-intercept and m is the coefficient, so if an equation has a negative coefficient, m<0. As a graph, the slope of the line is negative.