Question

Example 2 Identify the hypothesis and conclusion of each statement.

Then write each statement in if-then form.

$5m-8<52$when $m<12$.

Short answer

$5m-8<52$ is the hypothesis and $m<12$is the conclusion.

And if-then form is:

If $m<12$, then $5m-8<52$

Step-by-step solution

Step 1. Given expression.

$5m-8<52$when$m<12$

Step 2. Description of step.

To identify the hypothesis and conclusion in the statement

$5m-8<52$when $m<12$,

Solve the given expression and determine the values of m.

As,

$\begin{array}{l}5m-8<52\\ \Rightarrow 5m<52+8\\ \Rightarrow 5m<60\\ \Rightarrow m<\frac{60}{5}\\ \Rightarrow m<12\end{array}$

Now if m takes any value greater than 12, then the hypothesis $5m-8<52$becomes false.

And it is written in an if-then form as:

Thus, $5m-8<52$is the hypothesis and $m<12$is the conclusion.