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Here are the solutions to the questions: 23. The value of x in the equation 2x - 3 = 5 is Step 1: Add 3 to both sides of the equation. 2x - 3 + 3 = 5 + 3 2x = 8 Step 2: Divide both sides by 2. (2x)/(2) = (8)/(2) x = 4 The correct option is C. 4. 24. The value of x in the equation x^2 = 16 is Step 1: Take the square root of both sides of the equation. sqrt(x^2) = sqrt(16) x = ± 4 The correct option is D. ± 4. 25. The value of x in the equation 2x + 3 = 3x - 5 is Step 1: Subtract 2x from both sides of the equation. 2x + 3 - 2x = 3x - 5 - 2x 3 = x - 5 Step 2: Add 5 to both sides of the equation. 3 + 5 = x - 5 + 5 8 = x The correct option is A. 8. 26. The value of x in the inequality 2x - 1 < 5 is Step 1: Add 1 to both sides of the inequality. 2x - 1 + 1 < 5 + 1 2x < 6 Step 2: Divide both sides by 2. (2x)/(2) < (6)/(2) x < 3 The correct option is B. x < 3. 27. The solution to the simultaneous equations: x + y = 5 and x - y = 1 is Step 1: Add the two equations together to eliminate y. (x + y) + (x - y) = 5 + 1 2x = 6 Step 2: Solve for x. x = (6)/(2) x = 3 Step 3: Substitute the value of x into the first equation (x + y = 5). 3 + y = 5 Step 4: Solve for y. y = 5 - 3 y = 2 The solution is x=3, y=2. The correct option is A. x=3, y=2. 28. The value of x in the sequence 1, 3, 5, x, 9 is Step 1: Determine the common difference between consecutive terms. 3 - 1 = 2 5 - 3 = 2 This is an arithmetic sequence with a common difference d=2. Step 2: Find the value of x by adding the common difference to the preceding term. x = 5 + 2 x = 7 The correct option is B. 7. 29. The 10th term of the sequence 2, 4, 6, 8, is Step 1: Identify the first term (a) and the common difference (d). The first term a = 2. The common difference d = 4 - 2 = 2. Step 2: Use the formula for the n-th term of an arithmetic sequence, T_n = a + (n-1)d, with n=10. T_10 = 2 + (10-1)2 T_10 = 2 + (9)2 T_10 = 2 + 18 T_10 = 20 The correct option is C. 20. 30. The sum of the first 10 terms of the sequence 2, 4, 6, 8, is Step 1: Identify the first term (a), the common difference (d), and the number of terms (n). From question 29, a = 2, d = 2, and n = 10. Step 2: Use the formula for the sum of the first n terms of an arithmetic sequence, S_n = (n)/(2)(2a + (n-1)d). S_10 = (10)/(2)(2(2) + (10-1)2) S_10 = 5(4 + (9)2) S_10 = 5(4 + 18) S_10 = 5(22) S_10 = 110 The correct option is D. 110. 31. The common ratio of the sequence 2, 4, 8, 16, is Step 1: Calculate the ratio of any term to its preceding term. (4)/(2) = 2 (8)/(4) = 2 (16)/(8) = 2 The common ratio r = 2. The correct option is A. 2. 32. The 5th term of the sequence 2, 4, 8, 16, is Step 1: Identify the first term (a) and the common ratio (r). The first term a = 2. From question 31, the common ratio r = 2. Step 2: Use the formula for the n-th term of a geometric sequence, T_n = ar^n-1, with n=5. T_5 = 2 × 2^5-1 T_5 = 2 × 2^4 T_5 = 2 × 16 T_5 = 32 The correct option is B. 32. 33. The sum to infinity of the sequence 1, (1)/(2), (1)/(4), is Step 1: Identify the first term (a) and the common ratio (r). The first term a = 1. The common ratio r = (1/2)/(1) = (1)/(2). Step 2: Use the formula for the sum to infinity of a geometric sequence, S_ = (a)/(1-r), since |r| < 1. S_ = (1)/(1 - 1)2 S_ = (1)/(1)2 S_ = 1 × 2 S_ = 2 The correct option is A. 2. 34. The value of x in the equation _2 x = 3 is Step 1: Convert the logarithmic equation to its equivalent exponential form. The definition of logarithm states that _b a = c is equivalent to b^c = a. Here, b=2, a=x, and c=3. 2^3 = x Step 2: Calculate the value of 2^3. x = 2 × 2 × 2 x = 8 The correct option is D. 8. Last free one today — make it count tomorrow, or type /upgrade for unlimited.