Question

Tell whether each statement is true or false. Then write converse and tell whether it is true or false.

Statement: If $x=-6$,then$\left|x\right|=6$.

Short answer

The statement is true, but the converse is false.

Step-by-step solution

Step 1. Converse a conditional.

The converse of the conditional is obtained by interchanging the hypothesis and the conclusion. If p represents the hypothesis and q represents the conclusion, then converse of the statement “If p, then q” will be “If q, then p”.

Step 2. State whether the statement is true or not.

It is known that $\left|x\right|=-x$and $x=\left(-6\right)$.

Thus,

$\begin{array}{c}\left|x\right|=-\left(-6\right)\\ =6\end{array}$

Hence, the statement is true.

Step 3. Write the converse of the statement and verify.

The converse of the statement is: If $\left|x\right|=6$then $x=-6$, but if $\left|x\right|=6$, it means$x=\pm 6$.

Thus, the converse statement is false.

Therefore, the statement: "If $x=-6$, then $\left|x\right|=6$" is true, but the converse of the statement: "If $\left|x\right|=6$, then $x=-6$" is false.