Question

1. matt and kara solved the equation $8(x - 5) = 8x + 40$. kara said the answer was $x = 0$ and matt said there are no solutions. who is correct? support your answer with work.

Explanation:

Step 1: Expand the left side

We start by expanding the left - hand side of the equation \(8(x - 5)\) using the distributive property \(a(b - c)=ab - ac\). Here, \(a = 8\), \(b=x\) and \(c = 5\), so \(8(x - 5)=8x-40\). The original equation becomes \(8x-40=8x + 40\).

Step 2: Subtract \(8x\) from both sides

Subtract \(8x\) from both sides of the equation \(8x-40=8x + 40\). We get \((8x-8x)-40=(8x - 8x)+40\), which simplifies to \(- 40=40\).

Answer:

Since \(-40 = 40\) is a false statement, there are no solutions to the equation. So Matt is correct.