Determine the number that makes the following statement true: 53 - (a certain number) = 65.

4.1. Determine the number that makes the following statement true. 53 - (a certain number) = 65 Step 1: Let the certain number be x. 53 - x = 65 Step 2: Subtract 53 from both sides of the equation. -x = 65 - 53 -x = 12 Step 3: Multiply both sides by -1 to solve for x. x = -12 The certain number: -12 4.2.1. Calculate the following without the use of a calculator. (50 × 33 + 25 × 5)/(10 × 50 - 50 × 19) Step 1: Calculate the numerator. 50 × 33 + 25 × 5 = 1650 + 125 = 1775 Step 2: Calculate the denominator. Factor out 50. 10 × 50 - 50 × 19 = 50 × (10 - 19) = 50 × (-9) = -450 Step 3: Form the fraction and simplify. (1775)/(-450) Divide both numerator and denominator by their greatest common divisor, which is 25. 1775 ÷ 25 = 71 -450 ÷ 25 = -18 (71)/(-18) = -(71)/(18) The simplified value is -(71)/(18). 4.2.2. Calculate the following without the use of a calculator. -3 - (-2)(5) - (-4)^3 Step 1: Evaluate the multiplication term. (-2)(5) = -10 Step 2: Evaluate the exponential term. (-4)^3 = (-4) × (-4) × (-4) = 16 × (-4) = -64 Step 3: Substitute these values back into the expression. -3 - (-10) - (-64) Step 4: Simplify the double negative signs. -3 + 10 + 64 Step 5: Perform the additions from left to right. (-3 + 10) + 64 = 7 + 64 = 71 The value is 71. 4.2.3. Calculate the following without the use of a calculator. 3^3 - (-sqrt(4))^2 + [3]-64-4^2 × 1^3 + 17 Step 1: Evaluate the terms in the numerator. 3^3 = 3 × 3 × 3 = 27 (-sqrt(4))^2 = (-2)^2 = 4 [3]-64 = -4 (since (-4) × (-4) × (-4) = -64) Step 2: Substitute these values into the numerator and simplify. 27 - 4 + (-4) = 27 - 4 - 4 = 23 - 4 = 19 Step 3: Evaluate the terms in the denominator. -4^2 = -(4 × 4) = -16 1^3 = 1 × 1 × 1 = 1 Step 4: Substitute these values into the denominator and simplify. -16 × 1 + 17 = -16 + 17 = 1 Step 5: Form the fraction with the simplified numerator and denominator. (19)/(1) = 19 The value is 19.