Question

solve the following equation for x. express your answer in the simplest form. -2(-2x + 3) = 4x - 6

Explanation:

Step1: Expand the left side

We use the distributive property \(a(b + c)=ab+ac\). Here, \(a = - 2\), \(b=-2x\) and \(c = 3\). So \(-2(-2x + 3)=(-2)\times(-2x)+(-2)\times3 = 4x-6\). The equation becomes \(4x - 6=4x - 6\).

Step2: Subtract \(4x\) from both sides

Subtract \(4x\) from each side: \(4x-6 - 4x=4x - 6-4x\). This simplifies to \(-6=-6\).
Since we end up with a true statement (\(-6 = - 6\)) that is always true, regardless of the value of \(x\), the equation has infinitely many solutions.

Answer:

The equation has infinitely many solutions.