Solve: `6(1-4x)+7(2+5x)=53`. Check the result.

Answer

To solve the equation \( 6(1-4x) + 7(2+5x) = 53 \), we will follow these steps:

### Step 1: Distribute the terms inside the parentheses
We start by distributing the 6 and the 7 across their respective parentheses.

\[ 6(1) - 6(4x) + 7(2) + 7(5x) = 53 \]

This simplifies to:

\[ 6 - 24x + 14 + 35x = 53 \]

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

The constant terms are \(6\) and \(14\):

\[ 6 + 14 = 20 \]

The \(x\) terms are \(-24x\) and \(35x\):

\[ -24x + 35x = 11x \]

So, we can rewrite the equation as:

\[ 20 + 11x = 53 \]

### Step 3: Isolate the variable term
Now, we will isolate the term with \(x\) by subtracting \(20\) from both sides of the equation:

\[ 11x = 53 - 20 \]

This simplifies to:

\[ 11x = 33 \]

### Step 4: Solve for \(x\)
Next, we divide both sides by \(11\) to solve for \(x\):

\[ x = \frac{33}{11} \]

This simplifies to:

\[ x = 3 \]

### Step 5: Check the result
To verify our solution, we substitute \(x = 3\) back into the original equation:

\[ 6(1 - 4(3)) + 7(2 + 5(3)) = 53 \]

Calculating inside the parentheses:

\[ 6(1 - 12) + 7(2 + 15) = 53 \]

This simplifies to:

\[ 6(-11) + 7(17) = 53 \]

Calculating the products:

\[ -66 + 119 = 53 \]

Finally, we check if this is true:

\[ 53 = 53 \]

Since both sides are equal, our solution is verified.

### Final Answer:
\[ x = 3 \]

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