Question

15 3/8÷(2 3/4 х + 5 5/6) -1 1/2 =3/4

Answer 1

15 3/8÷(2 3/4 х + 5 5/6) -1 1/2 =3/4

(2 3/4 х + 5 5/6) -1 1/2 =123/4*4/3

2 3/4 х + 5 5/6 -1 1/2 =41

2 3/4 х =44+1 1/2-5 5/6

2 3/4x=42 1/2-5 5/6

2 3/4x=36 4/6

x=220/6*4/11

x=20/3*2=40/3=13 1/3

Answer 2

Let's break down the given equation step by step:

$15\frac{3}{8} \div (2\frac{3}{4}x + 5\frac{5}{6}) - 1\frac{1}{2} = \frac{3}{4}$.

First, let's simplify the equation by converting all the mixed numbers into improper fractions:

$15\frac{3}{8} = \frac{15 \times 8 + 3}{8} = \frac{123}{8}$,

$2\frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{11}{4}$,

$5\frac{5}{6} = \frac{5 \times 6 + 5}{6} = \frac{35}{6}$, and

$1\frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{3}{2}$.

Now the equation becomes:

$\frac{123}{8} \div \left(\frac{11}{4}x + \frac{35}{6}\right) - \frac{3}{2} = \frac{3}{4}$.

To solve for $x$, let's first simplify the expression inside the parentheses. To do this, find a common denominator for $\frac{11}{4}$ and $\frac{35}{6}$, which is 12. Rewrite the equation as:

$\frac{123}{8} \div \left(\frac{33}{12}x + \frac{70}{12}\right) - \frac{3}{2} = \frac{3}{4}$.

Now, combine the fractions inside the parentheses:

$\frac{123}{8} \div \left(\frac{33x + 70}{12}\right) - \frac{3}{2} = \frac{3}{4}$.

To divide by a fraction, multiply by its reciprocal:

$\frac{123}{8} \times \frac{12}{33x + 70} - \frac{3}{2} = \frac{3}{4}$.

Now, simplify further:

$\frac{61.5}{33x + 70} - \frac{3}{2} = \frac{3}{4}$.

To get rid of the fractions, multiply the entire equation by 4 to eliminate the fraction in $\frac{3}{4}$:

$4 \times \frac{61.5}{33x + 70} - 4 \times \frac{3}{2} = 4 \times \frac{3}{4}$.

$2(33x + 70) - 6 = 3$.

Expand and simplify:

$66x + 140 - 6 = 3$.

$66x + 134 = 3$