To solve this equation, we first need to simplify the expression on the left side of the equation:
4 3/8 ÷ 5 1/4
Convert the mixed numbers to improper fractions:
4 3/8 = (4*8 + 3)/8 = 35/8
5 1/4 = (5*4 + 1)/4 = 21/4
Now divide the fractions:
(35/8) ÷ (21/4) = (35/8) * (4/21) = 35/42 = 5/6
So, 4 3/8 ÷ 5 1/4 = 5/6
Now rewrite the original equation with the simplified value:
x / 12 * (3(2/5)x + 3) - (3/5)x = 8
Now, simplify the equation further:
x / 12 (3 + 3x/5) - (3/5)x = x/12 (15 + 3x) - (3/5)x = (x * (15 + 3x))/12 - (3x)/5 = (15x + 3x^2)/12 - (3x)/5 = (15x + 3x^2)/12 - (36x)/60 = (15x + 3x^2)/12 - (36x)/60 = (15x + 3x^2)/12 - (6x)/30 = (30x + 3x^2 - 72x) / 60 = (3x^2 - 42x) / 60 = 3x^2 - 42x = 483x^2 - 42x - 480 = 0
Now we have a quadratic equation, which can be solved by factoring, completing the square, or using the quadratic formula.
To solve this equation, we first need to simplify the expression on the left side of the equation:
4 3/8 ÷ 5 1/4
Convert the mixed numbers to improper fractions:
4 3/8 = (4*8 + 3)/8 = 35/8
5 1/4 = (5*4 + 1)/4 = 21/4
Now divide the fractions:
(35/8) ÷ (21/4) = (35/8) * (4/21) = 35/42 = 5/6
So, 4 3/8 ÷ 5 1/4 = 5/6
Now rewrite the original equation with the simplified value:
x / 12 * (3(2/5)x + 3) - (3/5)x = 8
Now, simplify the equation further:
x / 12 (3 + 3x/5) - (3/5)x =
x/12 (15 + 3x) - (3/5)x =
(x * (15 + 3x))/12 - (3x)/5 =
(15x + 3x^2)/12 - (3x)/5 =
(15x + 3x^2)/12 - (36x)/60 =
(15x + 3x^2)/12 - (36x)/60 =
(15x + 3x^2)/12 - (6x)/30 =
(30x + 3x^2 - 72x) / 60 =
(3x^2 - 42x) / 60 =
3x^2 - 42x = 48
3x^2 - 42x - 480 = 0
Now we have a quadratic equation, which can be solved by factoring, completing the square, or using the quadratic formula.