Chapter 3.3, Problem 43PPE

To determine

To find: The value of $\Delta$ so that make the inequalities equivalent.

Answer to Problem 43PPE

The $\Delta$ should be replaced by $-5.$ .

Explanation of Solution

Given information:

The inequalities:

  $\Delta x\ge 25$ and $x\le -5$

Calculation:

It is to be replaced $\Delta$ so that $-8u\le \Delta$ and $u\ge -0.5$ are equivalent. Here, left side coefficients of first and second inequality are -8 and -0.5 respectively. To get left side -8 of the second

Inequality, multiply the second inequality by $-8.$ Then

  $u\ge -0.5$

  $-8u\le -8(-0.5)$ (Multiply each side $-8.$ Reverse the inequality symbol)

  $-8u\le 4$

Therefore, $-8u\le 4$ and $u\ge -0.5$ are equivalent. But given that $-8u\le \Delta$ and $u\ge -0.5$ are equivalent. Hence, $\Delta$ should be replaced by 4.

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