Q36. - Algebra 1

Question

Example 4 Find a counterexample for each conditional statement.

If $3x+17\le 53$ then $x<12$.

Step-by-Step Solution

Answer

The statement that if $3x+17\le 53,$, then $x<12$ is not true and the counterexample is $x=12$.

Step 1. Given Statement.

$3x+17\le 53,$

Step 2. Description of step.

To find a counterexample for the given statement, solve the given expression and find the value of $x$ as

Step 3. Calculation.

$\begin{array}{l}3x+17\le 53\\ \Rightarrow 3x\le 53-17\\ \Rightarrow 3x\le 36\\ \Rightarrow x\le \frac{36}{3}\\ \Rightarrow x\le 12\end{array}$

But it is given in the statement that $x<12$.

But from the solution above it also satisfy for $x=12$, as

$\begin{array}{l}3x+17=3\left(12\right)+17\\ =36+17\\ =53\end{array}$

Since the statement is true for $x=12$ also.

Hence the statement that if $3x+17\le 53,$ then $x<12$ is not true, and counterexample is $x=12$.