Math Snap

STEP 1

1. The equation is $-14y + 12(-14y - 11) = 4418$.
2. We need to solve for the variable $y$.
3. The equation involves distributing and combining like terms.

STEP 2

1. Distribute the 12 across the terms inside the parentheses.
2. Combine like terms.
3. Isolate the variable $y$.
4. Solve for $y$.
5. Check the solution by substituting it back into the original equation.

STEP 3

Distribute the 12 across the terms inside the parentheses:
$$-14y + 12(-14y) + 12(-11) = 4418$$ This becomes:
$$-14y - 168y - 132 = 4418$$

STEP 4

Combine like terms on the left side of the equation:
$$(-14y - 168y) - 132 = 4418$$ This simplifies to:
$$-182y - 132 = 4418$$

STEP 5

Add 132 to both sides of the equation to isolate the terms with $y$:
$$-182y - 132 + 132 = 4418 + 132$$ This simplifies to:
$$-182y = 4550$$

STEP 6

Divide both sides by $-182$ to solve for $y$:
$$y = \frac{4550}{-182}$$ Simplify the fraction:
$$y = -25$$

Check the solution by substituting $y = -25$ back into the original equation:
$$-14(-25) + 12(-14(-25) - 11) = 4418$$ Calculate each term:
$$350 + 12(350 - 11) = 4418$$ $$350 + 12(339) = 4418$$ $$350 + 4068 = 4418$$ $$4418 = 4418$$ The left-hand side equals the right-hand side, confirming the solution is correct.
The solution is:
$$\boxed{-25}$$