Chapter 3.3, Problem 26PPE

To determine

To solve: the inequality $-7y\ge 17$ . Graph and check the solution.

Answer to Problem 26PPE

  $y\le -\frac{17}{7}$

Explanation of Solution

Given:

The inequality: $-7y\ge 17$

Concept Used:

Let a, b and c be real numbers where $c<0$ . Then,

If $a\ge b$ , then $\frac{a}{c}\le \frac{b}{c}$

Divide both sides of the given inequality by -7 (since, there is a division by a negative number so the sign of the inequality will be reversed),

  $\frac{-7y}{-7}\le \frac{17}{-7}$

Simplify both sides of the inequality,

  $y\le -\frac{17}{7}$

Now, to graph the inequality $y\le -\frac{17}{7}$ , draw a number line with a closed circle at $-\frac{17}{7}$ . And since y is less than or equal to $-\frac{17}{7}$ , so draw a line going towards left from the closed circle at $-\frac{17}{7}$ . Thus, the required graph is:

  

Now, to check the above solution, pick any number from the red line section of the above number line and substitute in given inequality,

So, let $y=-4$ . Then,

  $\begin{array}{c}-7\left(-4\right)\ge 17\\ 28\ge 17\end{array}$

Which is a true statement.

Conclusion:

Hence, the solution of the given inequality is $y\le -\frac{17}{7}$ .