Question

((4x+1)÷5)-((2x-3)÷3)=x-4

Answer 1

$((4x + 1) \div 5) - ((2x - 3) \div 3) = x - 4 \\ \frac{4x + 1}{5} - \frac{2x - 3}{3} = x - 4 \\ 3(4x + 1) - 5(2x - 3) = 15x - 60 \\ 12x + 3 - 10x + 15 = 15x - 60 \\ 2x + 18 = 15x - 60 \\ 2x - 15x = - 60 - 18 \\ - 13 = - 78 \\ x = \frac{ - 78}{ - 13} = 6$

Answer 2

To solve this equation, we need to simplify both sides and isolate the variable x. Let's start by simplifying the left side:

(4x + 1) ÷ 5 - (2x - 3) ÷ 3 = x - 4

Multiplying both sides by the least common multiple of the denominators, which is 15, we get:

3(4x + 1) - 5(2x - 3) = 15(x - 4)

Simplifying the left side by distributing the multiplication, we get:

12x + 3 - 10x + 15 = 15x - 60

Simplifying further by combining like terms, we get:

2x + 18 = 15x - 60

Bringing all the x terms to one side and all the constant terms to the other side, we get:

2x - 15x = -60 - 18

Simplifying:

-13x = -78

Finally, we can solve for x by dividing both sides by -13:

x = 6

Therefore, the solution to the equation is x = 6.