Question

$\frac{5x - 1}{12 } - \frac{x - 4}{5} = \frac{x + 7}{6}$
Solve this equation and verify the result​

Answer 1

Step 1. Multiply the numbers

           (5x - 1 . 1/12) - (x - 1 . 4/5) = x + 7/6

           (5x - 1/12) - (x - 1 . 4/5) = x + 7/6

           

Step 2. Multiply the numbers

            (5x - 1/12) - (x - 1 . 4/5) = x + 7/6

            (5x - 1/12) - (x - 4/5) = x + 7/6

Step 3. Distribute

            (5x - 1/2) - (x - 4/5) = x + 7/6

            (5x - 1/2) - x - 4/5 = x + 7/6

Answer 2

Answer:

$\frac{5x - 1}{12} - \frac{x - 4}{5} = \frac{x + 7}{6}$

Multiplying both sides of the given equation by 60 , the LCM of 12,5 and 6 we get

$( \frac{5x - 1}{12} ) \times 60 - ( \frac{x - 4}{5} ) \times 60 = \frac{ \times + 7}{6} \times 60$

5(5x -1) - 12(x-4) = 10 (x+7)

25x - 5 - 12x + 48 = 10x + 70

13x + 43 = 10x + 70

13x - 10x = 70 - 43 [transporting 10x to LHS and 43 to RHS]

3x = 27

$\frac{3x}{3} = \frac{27}{3} \\ x = 9$

Hence , x = 9 is the solution of the given equation.

Verification:-

substituting x = 9 in the given equation we get

$LHS = \frac{5 \times 9 - 1}{12} - \frac{9 - 4}{5} = \frac{44}{12} - \frac{5}{5} = \\ \\ \frac{11}{3} = 1 = \frac{11 - 3}{3} \\ = \frac{8}{3}$

LHS = RHS

the solution is thus checked for its correctness.