Question

1. find the mistake made in each scenario below and then solve for the correct solution: benny solved the following equation but has made a mistake. initial equation: 5(x + 8)-(x - 4)=x - 73 in which step did benny make a mistake? step 1 5x + 40 - x - 4=x - 73 a. between the initial equation and step 1 step 2 4x + 36=x - 73 b. between step 1 and step 2 step 3 3x + 36=-73 c. between step 2 and step 3 step 4 3x=-109 d. between step 3 and step 4 step 5 x=-36.3 e. between step 4 and step 5 describe the mistake benny made: what is the correct answer to the equation?

Explanation:

Step1: Expand the equation

Expand \(5(x + 8)-(x - 4)=x - 73\). Using the distributive property \(a(b + c)=ab+ac\), we get \(5x+40 - x + 4=x - 73\). Benny made a mistake in distributing the negative sign in \(-(x - 4)\), he wrote \(-x-4\) instead of \(-x + 4\). So the mistake is between the initial equation and Step 1.

Step2: Combine like - terms

Combining like - terms in \(5x+40 - x + 4=x - 73\), we have \((5x - x)+(40 + 4)=x - 73\), which simplifies to \(4x+44=x - 73\).

Step3: Isolate the \(x\) terms on one side

Subtract \(x\) from both sides: \(4x - x+44=x - x - 73\), resulting in \(3x+44=-73\).

Step4: Isolate the \(x\) term

Subtract 44 from both sides: \(3x+44 - 44=-73 - 44\), so \(3x=-117\).

Step5: Solve for \(x\)

Divide both sides by 3: \(x=\frac{-117}{3}=-39\).

Answer:

A. Between the Initial Equation and Step 1
Describe the mistake Benny made: Incorrect distribution of the negative sign in \(-(x - 4)\), should be \(-x + 4\) not \(-x-4\).
What is the correct answer to the equation? \(x=-39\)