Question

Check whether the given number is a solution of the inequality. $$ 16 p-9 \leq 71 ; 5 $$

Short answer

Yes, the given number 5 is a solution to the inequality.

Step-by-step solution

Solve the Inequality for 'p'

The given inequality is \(16p - 9 \leq 71\). First, add 9 to both sides of the inequality to isolate the term with 'p'. This yields: \(16p \leq 71 + 9\), which simplifies to: \(16p \leq 80\). To find 'p', divide both sides by 16, resulting in the inequality: \(p \leq 5\).

Test the Given Number

The number to be tested is 5. Substitute 5 for 'p' in the inequality \(p \leq 5\), resulting in: \(5 \leq 5\). Both sides of the inequality are equal, implying that 5 is indeed a solution to the inequality.