Solve Linear Equation: 11(-3x+4)-7(6x-2)=3 Step-by-Step

To solve the linear equation $11(-3x+4)-7(6x-2)=3$, follow these steps:

Begin by applying the distributive property to the expression on both sides:

• Distribute $11$: $11(-3x+4) = 11 \cdot (-3x) + 11 \cdot 4 = -33x + 44$.
• Distribute $-7$: $-7(6x-2) = -7 \cdot 6x + -7 \cdot (-2) = -42x + 14$.

Substitute these results back into the equation:

$-33x + 44 - 42x + 14 = 3$

Combine like terms:

$(-33x - 42x) + (44 + 14) = 3$

$-75x + 58 = 3$

Isolate the term with $x$ by subtracting 58 from both sides:

$-75x = 3 - 58$

$-75x = -55$

Now, solve for $x$ by dividing both sides by $-75$:

$x = \frac{-55}{-75}$

Simplify the fraction by dividing both numerator and denominator by 5:

$x = \frac{11}{15}$

Therefore, the solution to the equation is $\boxed{\frac{11}{15}}$.