−4(2x+1)+4x+3=−17

1 answer

To solve the equation \(-4(2x+1)+4x+3=-17\), we'll start by distributing the \(-4\) on the left-hand side:

\[ -4(2x) - 4(1) + 4x + 3 = -17 \]

This simplifies to:

\[ -8x - 4 + 4x + 3 = -17 \]

Next, combine like terms:

\[ (-8x + 4x) + (-4 + 3) = -17 \]

This simplifies to:

\[ -4x - 1 = -17 \]

Now, add \(1\) to both sides of the equation:

\[ -4x - 1 + 1 = -17 + 1 \]

Which simplifies to:

\[ -4x = -16 \]

Now, divide both sides by \(-4\):

\[ x = 4 \]

Thus, the solution to the equation is:

\[ \boxed{4} \]