Question

nicholas showed his friend alma the following problem from his homework. he told her that his answer was marked wrong but he could not find his mistake. alma told him that she found his mistake. what was nicholass mistake on this problem? step 1 2x - 3(x + 2)= - 8 step 2 2x - 3x + 2 = - 8 step 3 -x + 2 = - 8 step 4 -x = - 10 step 5 x = 10 alma said that there is a distribution error from step 1 to step 2. alma later decided that nicholas was correct; there were no errors in the solution of the problem. alma said that there is a subtraction error from step 3 to step 4. alma said that there is an addition error from step 2 to step 3.

Explanation:

Step1: Analyze step - 1 to step - 2

Starting with \(2x-3(x + 2)=-8\), distribute the \(-3\) using the distributive property \(a(b + c)=ab+ac\). We get \(2x-3x-6=-8\), not \(2x - 3x+2=-8\). So, there is a distribution error from step 1 to step 2.

Step2: Analyze step - 2 to step - 3

Combining like - terms in step 2 (\(2x-3x-6=-8\) gives \(-x-6=-8\), not \(-x + 2=-8\). But the error originated from the wrong distribution in step 1.

Step3: Analyze step - 3 to step - 4

If we had the correct step 2 \(-x-6=-8\), adding 6 to both sides gives \(-x=-2\), not \(-x=-10\). But again, the root error is from step 1.

Step4: Analyze step - 4 to step - 5

If \(-x=-10\) (from wrong step 4), then \(x = 10\). But the whole process is wrong due to the initial distribution error.

Answer:

Alma said that there is a distribution error from step 1 to step 2.