Q12. - Algebra 1

Question

Example 4 Find a counterexample for each conditional statement.

If $\left|x\right| = 7$ then $x=7$

Step-by-Step Solution

Answer

A counterexample is “If $\left|x\right|=7$, then $x=-7$”.

Step 1. Given.

If $\left|x\right|=7$ then $x=7$.

Step 2. To find.

We have to find the counterexample for the condition “If $\left|x\right|=7$ then $x=7$.”

Step 3. Calculation.

The given statement is: If $\left|x\right|=7$ then $x=7$

We know that $\left|x\right|$ can be negative or positive. So $\left|x\right|=7$ can mean $x=7$ or $x=–7$.

So, not necessarily true. Because $x=–7$ is also possible.