Question

3/4(1/6x-1/3)=3x-11 1/2

Answer 1

$\frac{3}{4} ( \frac{1}{6} x- \frac{1}{3} )=3x-11 \frac{1}{2} \\ \frac{1}{8} x- \frac{1}{4} =3x-11 \frac{1}{2} \\ \frac{1}{8} x-3x=-11 \frac{2}{4}+\frac{1}{4} \\ -2 \frac{7}{8} x=-11 \frac{1}{4} \\ x=-11 \frac{1}{4}:(-2 \frac{7}{8}) \\ x=3 \frac{21}{23}$

Answer 2

$\\\frac34(\frac16x-\frac13)=3x-11\frac12 \\ \\\frac18x-\frac14=3x-11\frac12 \\ \\\frac18x-3x=-11\frac12+\frac14 \\ \\-\frac{23}{8}x=-\frac{45}{4} /:(-\frac{23}{8}) \\ \\x=\frac{90}{23}=3\frac{21}{23}$

Answer 3

To solve the equation 3/4(1/6x - 1/3) = 3x - 11 1/2, we can follow these steps:

1. Distribute the 3/4 to the terms inside the parentheses:

   (3/4)(1/6x) - (3/4)(1/3) = 3x - 11 1/2

   (3/24)x - (3/12) = 3x - 11 1/2

   (1/8)x - (1/4) = 3x - 11 1/2

2. Simplify the fractions on both sides of the equation:

   (1/8)x - 1/4 = 3x - 23/2

3. Multiply all terms by 8 to eliminate the fractions:

   8 * [(1/8)x - 1/4] = 8 * (3x - 23/2)

   x - 2 = 24x - 92

   x - 24x = -92 + 2

   -23x = -90

4. Divide both sides by -23 to solve for x:

   x = (-90) / (-23)

   x ≈ 3.913

Therefore, the approximate solution to the equation is x ≈ 3.913.