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Unformatted text preview: w.petersons.com Inequalities 239 9. If x > 0 and y < 0, which of the following is always true? (A) x – y > y – x (B) x + y > 0 (C) xy > 0 (D) y > x (E) x – y < 0 10. In triangle ABC, AD is the altitude to BC. Then (A) (B) (C) (D) (E) AD > DC AD < BD AD > AC BD > DC AB > BD www.petersons.com 240 Chapter 14 SOLUTIONS TO PRACTICE EXERCISES
4x < 6 6 x< 4 3 Simplify to x < 2 6. (E) AB = CB + AC 7. (C) In right triangle ACB, the longest side is the hypotenuse AB. Therefore, side AC is less than AB. (D) A positive subtracted from a negative is always negative. (B) 2. (B) If equal quantities are added to unequal quantities, the sums are unequal in the same order.
c>d (+ ) a = b
a+c > b+d 8. 9. 3. (C) 3x4 < < 5 10 5 Multiply through by 10. 6 < x < 8 or x must be between 6 and 8. 4. (D) AB = CB + AC ∠ACB is the supplement of ∠ACD. Therefore, ∠ACB = 60°. ∠ABC must equal 70° because there are 180° in a triangle. Since ∠ABC is the largest angle in the triangle, AC must be the longest side. Therefore, AC > AB. 10. (D) In a right triangle, the largest angle is the right angle. Since ∠C is the largest angle, ∠C = 90°. If unequal quantities are subtracted from equal quantities, the results are unequal in the opposite order.
AC = AB ( − ) EC < DB
AE > AD or AD < AE 5. (C) If two angles of a triangle are unequal, the sides opposite these angles are unequal, with the larger side opposite the larger angle. Since ∠1 > ∠2, BC > AC. www.petersons.com Inequalities 241 Exercise 1
8 x < 10 x + 20 −2 x < 20 x > −10
−2 x < 12 x > −6 x + 10 > 50 x > 40 Exercise 2
1. (D) Angle A will contain 90°, which is the largest angle of the triangle. The sides from largest to smallest will be BC, AB, AC. (B) Since ∠SRT = ∠STR, ∠SRT will have to be greater than ∠PTR. Therefore, PT > PR in triangle PRT. (D) Angle ABC = 60°. Since ther...
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