Question

2 1/2 : (1/2 × X + 5/12) - 1 5/6 = 2/3

Answer 1

Ответ:

661/114

Пошаговое объяснение:

Более расширенный ответ дать не могу

Answer 2

Пошаговое объяснение:

2 1/2:(1/2×X+5/12)-1 5/6=2/3

5/2:(1/2×X+5/12)-11/6=2/3

5/2:((6x+5)/12)-11/6=2/3

5/2×12/(6x+5)-11/6=2/3

30/(6x+5)=2/3+11/6

30/(6x+5)=15/6

30/(6x+5)=5/2

5(6x+5)=30×2

30x+25=60

30x=60-25

30x=35

X=35/30=7/6=1 1/6

Answer 3

Let's solve the equation step by step:

$2 \frac{1}{2} : \left(\frac{1}{2}x + \frac{5}{12}\right) - 1 \frac{5}{6} = \frac{2}{3}$

First, let's deal with the division and subtraction inside the parentheses:

$2 \frac{1}{2} = \frac{5}{2}$

$1 \frac{5}{6} = \frac{11}{6}$

So, the equation becomes:

$\frac{5}{2} : \left(\frac{1}{2}x + \frac{5}{12}\right) - \frac{11}{6} = \frac{2}{3}$

Next, let's simplify the expression inside the parentheses:

$\frac{1}{2}x + \frac{5}{12} = \frac{6}{12}x + \frac{5}{12} = \frac{6x + 5}{12}$

Now, the equation looks like this:

$\frac{5}{2} : \frac{6x + 5}{12} - \frac{11}{6} = \frac{2}{3}$

To simplify further, let's convert the division into multiplication by the reciprocal:

$\frac{5}{2} \times \frac{12}{6x + 5} - \frac{11}{6} = \frac{2}{3}$

$\frac{30}{6x + 5} - \frac{11}{6} = \frac{2}{3}$

Next, let's get a common denominator for the fractions:

$\frac{30}{6x + 5} - \frac{22}{12} = \frac{2}{3}$

$\frac{30}{6x + 5} - \frac{22}{12} = \frac{2}{3}$

Now, combine the fractions:

$\frac{30}{6x + 5} - \frac{11}{6} = \frac{2}{3}$

To continue solving for $x$, we'll isolate $x$:

$\frac{30}{6x + 5} = \frac{2}{3} + \frac{11}{6}$

$\frac{30}{6x + 5} = \frac{4}{6} + \frac{11}{6}$

$\frac{30}{6x + 5} = \frac{15}{6}$

Cross-multiply:

$6 \cdot 30 = 15(6x + 5)$