Question

a) -3(x + 5) > 6
-3x - 5 > 6

Explanation:

Step1: Identify the error

The original step applied the distributive property incorrectly. When distributing \(-3\) over \((x + 5)\), it should be \(-3\times x + (-3)\times5=-3x - 15\), not \(-3x - 5\).

Step2: Correct the distribution

Starting with \(-3(x + 5)>6\), use the distributive property \(a(b + c)=ab+ac\) (here \(a = - 3\), \(b=x\), \(c = 5\)):
\(-3\times x+(-3)\times5>6\)
\(-3x-15>6\)

Step3: Solve the inequality

Add \(15\) to both sides:
\(-3x-15 + 15>6 + 15\)
\(-3x>21\)
Divide both sides by \(-3\) (remember to reverse the inequality sign):
\(x<-7\)

Answer:

The error was in the distributive property step. The correct first step after distributing is \(-3x - 15>6\), and the solution to the inequality is \(x < - 7\).