Question

how many solutions does this equation have? 4(-4z - 2) = -16z - 8 no solution one solution infinitely many solutions

Explanation:

Step1: Expand the left - hand side

We use the distributive property \(a(b + c)=ab+ac\). For \(4(-4z - 2)\), we have \(4\times(-4z)+4\times(-2)=-16z-8\). So the equation becomes \(-16z - 8=-16z - 8\).

Step2: Analyze the equation

If we add \(16z\) to both sides of the equation \(-16z - 8=-16z - 8\), we get \(- 8=-8\). This is a true statement that is independent of the value of \(z\). This means that any value of \(z\) will satisfy the original equation.

Answer:

infinitely many solutions