Q79. - Algebra 1

Question

Find a counterexample for each conditional statement.

 

If $\mathbf{4}\mathit{x}\mathbf{-}\mathbf{11}\mathbf{=}\mathbf{53}\mathbf{,}$ then $\mathit{x}\mathbf{<}\mathbf{16}$.

Step-by-Step Solution

Answer

The counter-example for the given statement is $x$.

Step 1. Given information.

We have a conditional statement ‘’$4x-11=53$, then $x<16$’’.

To find a counter-example of the given conditional statement.

Step 2. Counter-example.

Counter-example to any statement means any example which is making that statement is false.

Step 3. Conclusion.

The statement “If $4x-11=53$, then $x<16$”is a conditional statement then.

Solve the equation.

$\begin{array}{l}4x-11=53\\ 4x=53+11\\ 4x=64\\ x=16\end{array}$

As the $x$ be an exact number which is not in the given range of the $x$.

 

Therefore, the counter-example for the given statement is $x$.