Question

Give a counterexample to the following conditional statement. Write your answer as a number. If |x+ 4|= 8, then x=−12

Answer 1

he Solution:

iven in the question that if

`|x+4|=8\text{ then x=-12}`

We are required to give a counterexample to the given conditional statement above.

`\begin{gathered} |x+4|=8 \\ \text{Means that} \\ x+4=8\text{ or x+4=-8} \end{gathered}`

Solving each of the equations above, we get

`\begin{gathered} x+4=-8 \\ x=-8-4 \\ x=-12 \\ Or \\ x+4=8 \\ x=8-4 \\ x=4 \\ \text{ So, } \\ x=-12\text{ or x=4} \end{gathered}`

So, the counterexample to the given conditional statement is x = 4.