Solve the following eqations.Check your result in each case
`2x-3=3/10(5x-12)`

Answer

To solve the equation \( 2x - 3 = \frac{3}{10}(5x - 12) \), we will follow these steps:

### Step 1: Eliminate the fraction
Multiply both sides of the equation by 10 to eliminate the fraction:

\[ 10(2x - 3) = 10 \cdot \frac{3}{10}(5x - 12) \]

This simplifies to:

\[ 20x - 30 = 3(5x - 12) \]

### Step 2: Distribute on the right side
Now, distribute the 3 on the right side:

\[ 20x - 30 = 15x - 36 \]

### Step 3: Move all terms involving \( x \) to one side
Subtract \( 15x \) from both sides:

\[ 20x - 15x - 30 = -36 \]

This simplifies to:

\[ 5x - 30 = -36 \]

### Step 4: Move the constant term to the other side
Add 30 to both sides:

\[ 5x = -36 + 30 \]

This simplifies to:

\[ 5x = -6 \]

### Step 5: Solve for \( x \)
Now, divide both sides by 5:

\[ x = \frac{-6}{5} \]

### Step 6: Check the result
To check, substitute \( x = -\frac{6}{5} \) back into the original equation:

Left side:

\[ 2\left(-\frac{6}{5}\right) - 3 = -\frac{12}{5} - \frac{15}{5} = -\frac{27}{5} \]

Right side:

\[ \frac{3}{10}\left(5\left(-\frac{6}{5}\right) - 12\right) = \frac{3}{10}(-6 - 12) = \frac{3}{10}(-18) = -\frac{54}{10} = -\frac{27}{5} \]

Since both sides are equal, our solution is verified.

### Final Answer:
\[ x = -\frac{6}{5} \]

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