Question

1. francisco made only one mistake on his homework. describe the mistake he made and then solve the equation correctly.
2. quinn and logan solved the equation 8(x - 5)=8x + 40. quinn said the answer was x = 0 and logan said there were no solutions. who is correct? explain your reasoning.
3. nancy wrote two equivalent expressions. if she sets them equal to each other, will the equation have one solution, no solution or infinitely many solutions? use an example to support your answer.

Explanation:

Step1: Analyze Francisco's work

He started with the equation \(3(x - 7)=5x - 11\). His first - step error was in the distribution. When distributing 3 in \(3(x - 7)\), it should be \(3x-21\), not \(3x - 7\).

Step2: Correctly solve the equation

Start with \(3(x - 7)=5x - 11\).
Distribute: \(3x-21 = 5x - 11\).
Subtract \(3x\) from both sides: \(3x-3x - 21=5x-3x - 11\), which simplifies to \(-21 = 2x-11\).
Add 11 to both sides: \(-21 + 11=2x-11 + 11\), so \(-10 = 2x\).
Divide both sides by 2: \(\frac{-10}{2}=\frac{2x}{2}\), and \(x=-5\).

Answer:

Francisco made a mistake in the distribution step. The correct solution of the equation \(3(x - 7)=5x - 11\) is \(x = - 5\).