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# 4 x 40 x 10 5 d 03n 18 4 multiply by 100 3n

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Unformatted text preview: w.petersons.com Inequalities 239 9. If x &gt; 0 and y &lt; 0, which of the following is always true? (A) x – y &gt; y – x (B) x + y &gt; 0 (C) xy &gt; 0 (D) y &gt; x (E) x – y &lt; 0 10. In triangle ABC, AD is the altitude to BC. Then (A) (B) (C) (D) (E) AD &gt; DC AD &lt; BD AD &gt; AC BD &gt; DC AB &gt; BD www.petersons.com 240 Chapter 14 SOLUTIONS TO PRACTICE EXERCISES Diagnostic Test 1. (D) 4x &lt; 6 6 x&lt; 4 3 Simplify to x &lt; 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&gt;d (+ ) a = b a+c &gt; b+d 8. 9. 3. (C) 3x4 &lt; &lt; 5 10 5 Multiply through by 10. 6 &lt; x &lt; 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 &gt; 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 &lt; DB AE &gt; AD or AD &lt; 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 &gt; ∠2, BC &gt; AC. www.petersons.com Inequalities 241 Exercise 1 1. (A) 8 x &lt; 10 x + 20 −2 x &lt; 20 x &gt; −10 −2 x &lt; 12 x &gt; −6 x + 10 &gt; 50 x &gt; 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 &gt; PR in triangle PRT. (D) Angle ABC = 60°. Since ther...
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