Question

Solve the equation : 5(2-3x) - 17(2x - 5)=16​

Answer 1

Answer:

Given 5 (2 – 3x) -17 (2x – 5) = 16 On expanding the brackets, we get (5 × 2) – (5 × 3x) – (17 × 2x) + (17 × 5) = 16 10 – 15x – 34x + 85 = 16 10 + 85 – 34x – 15x = 16 95 – 49x = 16 Subtracting 95 from both sides, we get – 49x + 95 – 95 = 16 – 95 – 49x = -79 Dividing both sides by – 49, we get – 49x/ -49 = -79/-49 x = 79/49 Verification: Substituting x = (79/49) in LHS we get, 5 (2 – 3 × (79/49) – 17 (2 × (79/49) – 5) = 16 (5 × 2) – (5 × 3 × (79/49)) – (17 × 2 × (79/49)) + (17 × 5) = 16 10 – (1185/49) – (2686/49) + 85 = 16 (490 – 1185 – 2686 + 4165)/49 = 16 784/49 = 16 16 = 16 Therefore LHS = RHS Hence, verified.

Answer 2

$5(2 - 3x) - 17(2x - 5) = 16 \\ \\ = > 10 - 15x - 34x + 85 = 16 \\ \\ = > 10 + 85 - 15x - 34x = 16 \\ \\ = > 95 - 49x = 16 \\ \\ = > ( - 49x) = 16 - 95 \\ \\ = > ( - 49x) = (- 79) \\ \\ = > 49x = 79 \\ \\ = > \green{\boxed{ x = \frac{79}{49} }}$