Question

4 4/9:(2/3x+14)=5/17

Answer 1

Ответ:

2/3x + 14 = 4 4/9 : 5/17

2/3x + 14 = 40/9 * 17/5

2/3x + 14 = 136/9

2/3x = 136/9 - 14

2/3x = 136/9 - 126/9

2/3x = 10/9

x = 10/9 * 3/2

x = 5/3

x = 1 2/3

Answer 2

To solve the equation $\frac{4 \frac{4}{9}}{2/3x + 14} = \frac{5}{17}$, you can follow these steps:

Step 1: Convert the mixed number to an improper fraction.

$$4 \frac{4}{9} = \frac{4 \times 9 + 4}{9} = \frac{40}{9}$$

Step 2: Rewrite the equation with fractions:

$$\frac{\frac{40}{9}}{\frac{2}{3}x + 14} = \frac{5}{17}$$

Step 3: Invert and multiply to get rid of the fraction in the denominator:

$$\frac{40}{9} \times \frac{17}{5} = \frac{2}{3}x + 14$$

Solve for $x$:

$$\frac{680}{45} = \frac{2}{3}x + 14$$

Step 4: Simplify and solve for $x$:

$$\frac{680}{45} - 14 = \frac{2}{3}x$$

$$\frac{680}{45} - \frac{630}{45} = \frac{2}{3}x$$

$$\frac{50}{45} = \frac{2}{3}x$$

$$\frac{10}{9} = \frac{2}{3}x$$

$$x = \frac{10}{9} \times \frac{3}{2}$$

$$x = \frac{15}{9}$$

$$x = \frac{5}{3}$$

So the solution to the equation is $x = \frac{5}{3}$.