Chapter 4: Q. 43 (page 246)

Solve each inequality. Graph the solution set.
$\frac{2 x - 6}{1 - x} < 2$

Short Answer

Expert verified

The real zeroes are 1 and 2 and the solution set can be graphed as

Step by step solution

Step 1. Given Information

The given inequality is $\frac{2 x - 6}{1 - x} < 2$

Step 2. Calculation

Solve the given inequality as follows,

$\frac{2 x - 6}{1 - x} - 2 < 2 - 2 \frac{2 x - 6}{1 - x} - 2 < 0 \frac{2 x - 6}{1 - x} - 2 (\frac{1 - x}{1 - x}) < 0 \frac{4 x - 8}{1 - x} < 0$

Now, let $f (x) = \frac{4 x - 8}{1 - x}$ . We will find the real zeroes of the numerator and denominator.

$4 x - 8 = 0 \Rightarrow x = 2 1 - x = 0 \Rightarrow x = 1$

Thus, real zeroes of the function are 1 and 2

Step 3. Graph

Construct the table by using a number from each interval to check whether the function is positive or negative.

Thus, the solution set is $\{x | x < - 1 o r x > 2\}$

And the solution set can be graphed as

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Solve each inequality. Graph the solution set.
$\frac{2 x - 6}{1 - x} < 2$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

Step 3. Graph

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Solve each inequality. Graph the solution set.2x-61-x<2

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

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One App. One Place for Learning.

Most popular questions from this chapter

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Solve each inequality. Graph the solution set.
$\frac{2 x - 6}{1 - x} < 2$