Question

1. noor and eve each solved the equation $5(x - 10) = 45$ and got different solutions. the table shows their work.

noor’s work	eve’s work

a. who is correct? explain.

Explanation:

To determine who is correct, we analyze both solutions. For Noor: Starting with \(5(x - 10)=45\), she recognizes that \(5\times9 = 45\), so \(x - 10=9\). Solving \(x - 10 = 9\) gives \(x=19\) (since \(19 - 10 = 9\)). For Eve: When distributing \(5\) into \((x - 10)\), the correct distribution is \(5x-50\), not \(5x - 10\). Eve made a mistake in the distributive property (forgot to multiply \(5\) by \(10\)). So Noor's steps are correct as she correctly identified the value of \((x - 10)\) by using the fact that \(5\times9 = 45\) and then solved for \(x\) properly.

Answer:

Noor is correct. Eve made a mistake in the distributive property (wrote \(5x - 10\) instead of \(5x-50\)) when expanding \(5(x - 10)\). Noor correctly determined \(x - 10 = 9\) (since \(5\times9 = 45\)) and then solved \(x-10 = 9\) to get \(x = 19\), which satisfies the original equation \(5(19 - 10)=5\times9 = 45\).