Questions: Solve and check the equation. 4 = -3(x-4) - (-4x+3) A. 13 B. 5 C. -5 D. -11

Solution Steps

To solve the equation \(4 = -3(x-4) - (-4x + 3)\), we need to simplify both sides of the equation and solve for \(x\). We will then check which of the given options satisfies the equation.

We start with the equation: \[ 4 = -3(x-4) - (-4x + 3) \]

First, distribute the \(-3\) and the negative sign: \[ 4 = -3x + 12 + 4x - 3 \]

Combine like terms: \[ 4 = x + 9 \]

To isolate \(x\), subtract 9 from both sides: \[ 4 - 9 = x \] \[ -5 = x \]

We substitute \(x = -5\) back into the original equation to verify: \[ 4 = -3(-5-4) - (-4(-5) + 3) \] \[ 4 = -3(-9) - (20 + 3) \] \[ 4 = 27 - 23 \] \[ 4 = 4 \]

The solution satisfies the original equation.

Final Answer