Answer : |2x – 3| < 1 Square both sides ⇒ (2x – 3)2 < 12 ⇒ 4x2 – 12x + 9 < 1 ⇒ 4x2 – 12x + 8 < 0 Divide throughout by 4 ⇒ x2 – 3x + 2 < 0 ⇒ x2 – 2x – x + 2 < 0 ⇒ x(x – 2) – 1(x –...
Find the solution set of the in equation |2x – 3| < 1.
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Excercise 6A
To receive grade A in a course one must obtain an average of 90 marks or more in five papers, each of 100 marks. If Tanvy scored 89, 93, 95 and 91 marks in first four papers, find the minimum marks that she must score in the last paper to get grade A in the course.
Answer : Let x marks be scored by Tanvy in her last paper. It is given that Tanvy scored 89, 93, 95 and 91 marks in first 4 papers. To receive grade A, she must obtain an average of 90 marks or...
How many litres of water will have to be added to 600 litres of the 45% solution of acid so that the resulting mixture will contain more than 25%, but less than 30% acid content?
Answer : Let x litres of water be added. Then total mixture = x + 600 Amount of acid contained in the resulting mixture is 45% of 600 litres. It is given that the resulting mixture contains more...
A manufacturer has 640 litres of an 8% solution of boric acid. How many litres of 2% boric and acid solution be added to it so that the boric acid content in the resulting mixture will be more than 4% but less than 6%.
Answer : Let x litres of 2% boric and acid solution be added to 640 litres of 8% solution of boric acidl
The watering acidity in a pool is considered normal when the average pH reading of three daily measurements is between 8.2 and 8.5. If the first two pH reading 8.48 and 8.35, find the range of the pH values for the third reading that will result in the acidity level is normal.
Answer : Let x be the third pH value. Now, it is given that the average pH reading of three daily measurements is between 8.2 and 8.5 Also, the first two pH readings are 8.48 and 8.35 Therefore, 8.2...
A company manufactures cassettes. Its cost and revenue function are C(x) = 25000 + 30x and R(x) = 43x respectively, where x is the number of cassettes produced and sold in a week. How many cassettes must be sold by the company to realize some profit?
Answer : Given: Cost function C(x) = 25000 + 30x Revenue function R(x) = 43x To Find: Number of cassettes to be sold to realize some profit In order, to gain profit: R(x) > C(x) Therefore, 43x...
Find all pairs of consecutive even positive integers both of which are larger than 8 such that their sum is less than 25.
Answer : Let the pair of consecutive even positive integers be x and x + 2. So, it is given that both the integers are greater than 8 Therefore, x > 8 and x + 2 > 8 When, x + 2 > 8...
Find all pairs of consecutive even positive integers both of which are larger than 8 such that their sum is less than 25.
Answer : Let the pair of consecutive even positive integers be x and x + 2. So, it is given that both the integers are greater than 8 Therefore, x > 8 and x + 2 > 8 When, x + 2 > 8...
Solve the following systems of linear in equations: 1 ≤ |x – 2| ≤ 3
Answer : 1 ≤ |x - 2| and |x - 2| ≤ 3 When, |x - 2| ≥ 1 Then, x – 2 ≤ -1 and x -2 ≥ 1 Now when, x – 2 ≤ - 1 Adding 2 to both the sides in above equation x – 2 + 2 ≤ -1 + 2 x ≤ 1 Now when, x – 2 ≥ 1...
Solve the following systems of linear in equations:
Solve the following systems of linear in equations:
Solve the following systems of linear in equations: 3x – x > x + > 3
Answer : 3x – x > 2 and x > 3 When, 3x – x > x Subtracting x from both the sides in above equation 2x – x > x + - x Multiplying both the sides by 3 in the above equation 3x > 3...
Solve the following systems of linear in equations: 5x – 7 < (x + 3), 1 – x – 4
Answer : When, 5x – 7 < x + 3 Adding 7 to both the sides in the above equation 5x – 7 + 7 < x + 3 + 7 5x < x + 10 Now, subtracting x from both the sides 5x – x < x + 10 -x 4x < 10...
Solve the following systems of linear in equations: –11 ≤ 4x – 3 ≤ 13
Answer : -11 ≤ 4x – 3 and 4x – 3 ≤ 13 When, -11 ≤ 4x - 3 4x – 3 ≥ -11 Adding 3 to both the sides 4x – 3 + 3 ≥ -11 + 3 4x ≥ - 8 Divide both the sides by 4 in above equation x ≥ -2 Now when, 4x – 3 ≤...
Solve the following systems of linear in equations:
Solve each of the following in equations and represent the solution set on the number line. x – 4 > 1, x ≠ 4.
Answer : Given: > 1, x ≠ 4. Adding 4 to both the sides in above equation x – 4 + 4 > 1 + 4 x > 5 Therefore, x є (5, ∞)
Solve each of the following in equations and represent the solution set on the number line. |x + a| + |x| > 3, x ϵ R.
Answer : Given: |x + a| + |x| > 3, x ϵ R. |x + a| = -(x + a) or (x + a) |x| = -x or x When |x + a| = -(x + a) and |x| = -x Then, |x + a| + |x| > 3 → -(x + a) + (-x) > 3 -x -a – x > 3 -2x...