4/5(15x+20)-7x=5/6(12x-24)+6

To solve this equation, we will begin by simplifying both sides of the equation:

Starting with the left side:

4/5(15x+20)-7x

Distribute the 4/5 to both terms inside the parentheses:

(4/5)(15x) + (4/5)(20) - 7x

Simplify the expressions inside the parentheses:

(12x) + (16) - 7x

Combine like terms:

12x - 7x + 16

Simplify further:

5x + 16

Moving onto the right side of the equation:

5/6(12x-24) + 6

Distribute the 5/6 to both terms inside the parentheses:

(5/6)(12x) + (5/6)(-24) + 6

Simplify the expressions inside the parentheses:

(10x) + (-20) + 6

Combine like terms:

10x - 14

Now, we can rewrite the equation with our simplified expressions:

5x + 16 = 10x - 14

Next, we will isolate the variable on one side of the equation. Let's move the 10x term to the left side by subtracting 10x from both sides:

5x + 16 - 10x = 10x - 14 - 10x

Simplify:

-5x + 16 = -14

To eliminate the constant term on the right side, we can subtract 16 from both sides:

-5x + 16 - 16 = -14 - 16

Simplify:

-5x = -30

To solve for x, we will divide both sides by -5:

(-5x)/-5 = (-30)/-5

Simplify:

x = 6

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