Question

5/8*(1/3x-5/6)+3/4*(1/2x+3/4)= -1/4

Answer 1

5/24x-25/48+3/8x+9/16=-1/4
5/24x+3/8x=-1/4-9/16+25/48
5/24x+9/24x=-12/48-27/48+25/48
7/12x=-14/48
x=-14/48:7/12=-14/48*12/7
x=-1/2

Answer 2

To solve the equation, we need to find the value of "x" that satisfies the equation:

$\frac{5}{8} \left( \frac{1}{3}x - \frac{5}{6} \right) + \frac{3}{4} \left( \frac{1}{2}x + \frac{3}{4} \right) = -\frac{1}{4}$

Let's start by simplifying the equation step-by-step:

Step 1: Distribute the coefficients inside the parentheses.

$\frac{5}{8} \cdot \frac{1}{3}x - \frac{5}{8} \cdot \frac{5}{6} + \frac{3}{4} \cdot \frac{1}{2}x + \frac{3}{4} \cdot \frac{3}{4} = -\frac{1}{4}$

Step 2: Multiply the fractions.

$\frac{5}{24}x - \frac{25}{48} + \frac{3}{8}x + \frac{9}{16} = -\frac{1}{4}$

Step 3: Combine like terms.

$\left( \frac{5}{24}x + \frac{3}{8}x \right) - \frac{25}{48} + \frac{9}{16} = -\frac{1}{4}$

Step 4: Add the fractions with a common denominator.

$\frac{15}{24}x - \frac{25}{48} + \frac{27}{48} = -\frac{1}{4}$

Step 5: Combine the fractions on the left side.

$\frac{15}{24}x + \frac{2}{48} = -\frac{1}{4}$

Step 6: Simplify further.

$\frac{15}{24}x + \frac{1}{24} = -\frac{1}{4}$

Step 7: Subtract $\frac{1}{24}$ from both sides to isolate $x$.

$\frac{15}{24}x = -\frac{1}{4} - \frac{1}{24}$

Step 8: Find a common denominator and add the fractions on the right side.

$\frac{15}{24}x = -\frac{6}{24}$

Step 9: Now, isolate $x$ by dividing both sides by $\frac{15}{24}$.

$x = \frac{-6}{24} \div \frac{15}{24}$

Step 10: When dividing fractions, invert the second fraction and multiply.

$x = \frac{-6}{24} \times \frac{24}{15}$

Step 11: Simplify the fraction.

$x = \frac{-1}{5}$