12:I[9616,["/_next/static/chunks/05-i_dhy86cw1.js","/_next/static/chunks/2qwpo-ux3i104.js","/_next/static/chunks/3fa8e1maunl2f.js","/_next/static/chunks/11g3xuiafo48i.js","/_next/static/chunks/0dz8bp0ruboce.js","/_next/static/chunks/1k4x3ofzy42np.js","/_next/static/chunks/1k_-ipk9babwa.js","/_next/static/chunks/243mwg64_2v8w.js"],"default"] 13:I[44184,["/_next/static/chunks/05-i_dhy86cw1.js","/_next/static/chunks/2qwpo-ux3i104.js","/_next/static/chunks/3fa8e1maunl2f.js","/_next/static/chunks/11g3xuiafo48i.js","/_next/static/chunks/0dz8bp0ruboce.js","/_next/static/chunks/1k4x3ofzy42np.js","/_next/static/chunks/1k_-ipk9babwa.js","/_next/static/chunks/243mwg64_2v8w.js"],"default"] 14:T54e,Explanatory Answer We have to find the values of "x" that will satisfy the four inequalities given in the answer choices and identify the choice for which the range of values satisfying it is finite. Choice A: x2 + 5x + 6 > 0 Factorize the given equation: x2 + 5x + 6 > 0 = (x + 2)(x + 3) > 0. This inequality will hold good when both (x + 2) and (x + 3) are simultaneously positive or simultaneously negative. Evaluating both the options, we get the range of values of "x" that satisfy this inequality to be x < -2 or x > -3. i.e., "x" does not lie between -2 and -3. i.e., x takes values lesser than 2 or greater than 3. The range of values that x takes is infinite. Choice B: |x + 2| > 4 |x + 2| > 4 is a modulus function and therefore, has two options Option 1: x + 2 > 4 or Option 2: (x + 2) < -4. Evaluating the two options we get the values of "x" that satisfy the inequality as x > 2 and x < -6. i.e., "x" does not lie between -6 and 2. An infinite range of values. Choice C: 9x - 7 < 3x + 14 Simplifying, we get 6x < 21 or x < 3.5. An infinite range of values. Choice D: x2 - 4x + 3 < 0 Factorizing x2 - 4x + 3 < 0 we get, (x - 3)(x - 1) < 0. This inequality will hold good when one of the terms (x - 3) or (x - 1) is positive and the other is negative. Evaluating both the options, we get 1 < x < 3. i.e., a finite range of values for "x". Choice D

If "x" is an integer, which of the following inequalities have a…