Question

5/6(0,5x-2/3)=3x-2,25​

Answer 1

5/6*(1/2х * 2/3) = 3х-9/4
5/12х-5/9=3х-9/4 ( умножить обе части на 36)
15х-20=108х-81
15х-108х=-81+20
-93х=-61
х= 61/93

Answer 2

To solve the equation $\frac{5}{6}(0.5x - \frac{2}{3}) = 3x - 2.25$, we'll follow these steps:

1. Distribute the $\frac{5}{6}$ on the left side of the equation.
2. Simplify both sides of the equation.
3. Solve for $x$.

Let's start:

Step 1: Distribute the $\frac{5}{6}$ on the left side of the equation: $\frac{5}{6} \cdot 0.5x - \frac{5}{6} \cdot \frac{2}{3} = 3x - 2.25$

Step 2: Simplify both sides of the equation: $\frac{5}{12}x - \frac{5}{9} = 3x - 2.25$

Step 3: Solve for $x$: First, let's get rid of the fractions by multiplying both sides of the equation by the least common multiple (LCM) of 12 and 9, which is 36: $36 \cdot (\frac{5}{12}x - \frac{5}{9}) = 36 \cdot (3x - 2.25)$

This simplifies to: $15x - 20 = 108x - 81$

Now, let's isolate $x$: Subtract 15x from both sides: $-20 = 93x - 81$

Add 81 to both sides: $61 = 93x$

Finally, divide both sides by 93: $x = \frac{61}{93}$

Now we can simplify the fraction if needed: x \approx 0.655 \

So, the solution to the equation is approximately $x \approx 0.655$.