Solve the following equations.Check your result in each case
`2.4(3-x)-0.6(2x-3)=0`

Answer

To solve the equation \(2.4(3-x) - 0.6(2x-3) = 0\), we will follow these steps:

### Step 1: Distribute the terms
We start by distributing \(2.4\) and \(-0.6\) into their respective brackets.

\[ 2.4 \cdot 3 - 2.4 \cdot x - 0.6 \cdot 2x + 0.6 \cdot 3 = 0 \]

Calculating these gives:

\[ 7.2 - 2.4x - 1.2x + 1.8 = 0 \]

### Step 2: Combine like terms
Next, we combine the constant terms and the \(x\) terms.

The constant terms are \(7.2\) and \(1.8\):

\[ 7.2 + 1.8 = 9 \]

The \(x\) terms are \(-2.4x\) and \(-1.2x\):

\[ -2.4x - 1.2x = -3.6x \]

So, we can rewrite the equation as:

\[ 9 - 3.6x = 0 \]

### Step 3: Isolate the variable
Now, we want to isolate \(x\). We can do this by moving \(9\) to the other side of the equation:

\[ -3.6x = -9 \]

### Step 4: Solve for \(x\)
Now, divide both sides by \(-3.6\):

\[ x = \frac{-9}{-3.6} = \frac{9}{3.6} \]

To simplify \(\frac{9}{3.6}\):

\[ x = 2.5 \]

### Step 5: Check your result
To verify our solution, we will substitute \(x = 2.5\) back into the original equation:

\[ 2.4(3 - 2.5) - 0.6(2(2.5) - 3) = 0 \]

Calculating inside the brackets:

\[ 2.4(0.5) - 0.6(5 - 3) = 0 \]

Calculating further:

\[ 1.2 - 0.6 \cdot 2 = 0 \]

\[ 1.2 - 1.2 = 0 \]

Since both sides equal \(0\), our solution is verified.

### Final Answer
Thus, the solution to the equation \(2.4(3-x) - 0.6(2x-3) = 0\) is:

\[ \boxed{2.5} \]