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