Find all values of $x$ that satisfy the inequality $\dfrac{2x-3}{(x-2)(x-4)}<0$.

Find all values of x that satisfy the inequality (2x-3)/((x-2)(x-4))<0.

Exercise 2.8 · Q2

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Step 1. Critical points: $x=\dfrac32$ (numerator zero), $x=2,4$ (denominator zero, excluded).

Step 2. Test each interval. $x=0$ : $\dfrac{-3}{(-2)(-4)}=\dfrac{-3}{8}<0$ . $x=1.75$ : $\dfrac{0.5}{(-0.25)(-2.25)}>0$ . $x=3$ : $\dfrac{3}{(1)(-1)}=-3<0$ . $x=5$ : $\dfrac{7}{(3)(1)}>0$ . …

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Q.Find all values of $x$ that satisfy the inequality $\dfrac{2x-3}{(x-2)(x-4)}<0$ .

Concept understanding — Rational Inequalities

Q.Find all values of xxx that satisfy the inequality 2x−3(x−2)(x−4)<0\dfrac{2x-3}{(x-2)(x-4)}<0(x−2)(x−4)2x−3​<0.

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Q.Find all values of $x$ that satisfy the inequality $\dfrac{2x-3}{(x-2)(x-4)}<0$ .

Unlock everything free for 14 days