This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here is the solution for question 6 from the image. 6a) Solve the inequality (2(x-2))/(5) - (1(x+5))/(6) < 0 Step 1: Find a common denominator for the fractions. The least common multiple of 5 and 6 is 30. Multiply the first fraction by (6)/(6) and the second fraction by (5)/(5). (6 · 2(x-2))/(6 · 5) - (5 · 1(x+5))/(5 · 6) < 0 (12(x-2))/(30) - (5(x+5))/(30) < 0 Step 2: Combine the fractions over the common denominator. (12(x-2) - 5(x+5))/(30) < 0 Step 3: Expand the terms in the numerator. (12x - 24 - 5x - 25)/(30) < 0 Step 4: Combine like terms in the numerator. ((12x - 5x) + (-24 - 25))/(30) < 0 (7x - 49)/(30) < 0 Step 5: Multiply both sides by 30 to clear the denominator. 7x - 49 < 0 Step 6: Add 49 to both sides. 7x < 49 Step 7: Divide both sides by 7. x < (49)/(7) x < 7 The final answer for 6a) is x < 7. 6b) By rationalizing the denominator, simplify 7sqrt(5)sqrt(7) Step 1: To rationalize the denominator, multiply the numerator and the denominator by sqrt(7). 7sqrt(5)sqrt(7) × sqrt(7)sqrt(7) Step 2: Multiply the numerators and the denominators. 7sqrt(5) · sqrt(7)sqrt(7) · sqrt(7) 7sqrt(5 · 7)7 7sqrt(35)7 Step 3: Simplify the expression by canceling out the common factor of 7. sqrt(35) The final answer for 6b) is sqrt(35).