Solve: `16(3x-5)-10(4x-8)=10`. Check the result.

Answer

To solve the equation \( 16(3x - 5) - 10(4x - 8) = 10 \), we will follow these steps:

### Step 1: Distribute the terms
Distributing \( 16 \) and \( -10 \) across their respective brackets:

\[ 16(3x) - 16(5) - 10(4x) + 10(8) = 10 \]

This simplifies to:

\[ 48x - 80 - 40x + 80 = 10 \]

### Step 2: Combine like terms
Now, combine the like terms on the left side:

\[ (48x - 40x) + (-80 + 80) = 10 \]

This simplifies to:

\[ 8x + 0 = 10 \]

So we have:

\[ 8x = 10 \]

### Step 3: Solve for \( x \)
Now, divide both sides by \( 8 \):

\[ x = \frac{10}{8} \]

This simplifies to:

\[ x = \frac{5}{4} \]

### Step 4: Check the result
To check our solution, substitute \( x = \frac{5}{4} \) back into the original equation:

\[ 16(3(\frac{5}{4}) - 5) - 10(4(\frac{5}{4}) - 8) = 10 \]

Calculating inside the brackets:

\[ 3(\frac{5}{4}) = \frac{15}{4} \quad \text{and} \quad 4(\frac{5}{4}) = 5 \]

So we have:

\[ 16(\frac{15}{4} - 5) - 10(5 - 8) = 10 \]

Now, calculate \( \frac{15}{4} - 5 \):

\[ 5 = \frac{20}{4} \quad \Rightarrow \quad \frac{15}{4} - \frac{20}{4} = -\frac{5}{4} \]

Now substitute back into the equation:

\[ 16(-\frac{5}{4}) - 10(-3) = 10 \]

Calculating:

\[ -16 \cdot \frac{5}{4} = -20 \quad \text{and} \quad -10 \cdot -3 = 30 \]

So we have:

\[ -20 + 30 = 10 \]

This confirms that the left side equals the right side, thus verifying our solution.

### Final Answer:
\[ x = \frac{5}{4} \]

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