(a) Solve the inequality: \(\frac{1 +…

Question 1 Report

(a) Solve the inequality: \(\frac{1 + 4x}{2}\) -\(\frac{5 + 2x}{7}\) < x -2

(b) If x: y = 3: 5, find the value of \(\frac{2x^2 - y^2}{y^2 - x^2}\)

Answer

Answer Details

(a) Solve \(\dfrac{1+4x}{2}-\dfrac{5+2x}{7}\[7(1+4x)-2(5+2x)<14(x-2)\]\[7+28x-10-4x<14x-28\]\[24x-3<14x-28\]\[24x-14x<-28+3\]\[10x<-25\Rightarrow x<-2.5\]

\(x<-2.5\)

(b) \(x:y=3:5\), so let \(x=3k,\ y=5k\).

\[\frac{2x^{2}-y^{2}}{y^{2}-x^{2}}=\frac{2(3k)^{2}-(5k)^{2}}{(5k)^{2}-(3k)^{2}}=\frac{2(9k^{2})-25k^{2}}{25k^{2}-9k^{2}}=\frac{18k^{2}-25k^{2}}{16k^{2}}=\frac{-7k^{2}}{16k^{2}}=-\frac{7}{16}\]

\(\dfrac{2x^{2}-y^{2}}{y^{2}-x^{2}}=-\dfrac{7}{16}\)

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(a) Solve the inequality: \(\frac{1 + 4x}{2}\) -\(\frac{5 + 2x}{7}\) < x -2 (b) If x: y = 3: 5, find the value of \(\frac{2x^2 - y^2}{y^2 - x^2}\)

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