Chapter 3: Q. 21 (page 171)

In Problems 7–22, solve each inequality.
$6 (x^{2} - 1) > 5 x$

Short Answer

Expert verified

The solution set is $\{x : x < \frac{- 2}{3} or x > \frac{3}{2}\}$ .

Step by step solution

Step 1. Given Information

The given inequality is $6 (x^{2} - 1) > 5 x$ .

Step 2. Find the Intercepts and Vertex

Express the inequality in standard form.

$6 x^{2} - 5 x - 6 > 0$

Factor the function $f (x) = 6 x^{2} - 5 x - 6$ .

$f (x) = (2 x - 3) (3 x + 2)$

So, the x-intercept of the function are $(\frac{3}{2}, 0), (- \frac{2}{3}, 0)$ .
The value of $f (0) = - 6$ .
So, the y-intercept is $(0, - 6)$ .
Find x -coordinate of the vertex by using the formula $x = \frac{- b}{2 a}$ .

$x = \frac{5}{12}$

The value of $f (\frac{5}{12}) = \frac{- 169}{24}$ .
So, the vertex of the parabola is $(\frac{5}{12}, \frac{- 169}{24})$ ..

Step 3. Plot the Function

Plot the curve of the function on the graph by using the obtained vertices and intercepts.

Step 4. Find the region above x-axis

From the graph, it is observed that the curve is above x-axis when $x < \frac{- 2}{3} or x > \frac{3}{2}$ .
So, the solution set is $\{x : x < \frac{- 2}{3} or x > \frac{3}{2}\}$

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In Problems 7–22, solve each inequality.
$6 (x^{2} - 1) > 5 x$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find the Intercepts and Vertex

Step 3. Plot the Function

Step 4. Find the region above x-axis

One App. One Place for Learning.

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In Problems 7–22, solve each inequality.6(x2-1)>5x

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find the Intercepts and Vertex

Step 3. Plot the Function

Step 4. Find the region above x-axis

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Probability and Statistics

Statistics

Pure Maths

Logic and Functions

Decision Maths

Study anywhere. Anytime. Across all devices.

In Problems 7–22, solve each inequality.
$6 (x^{2} - 1) > 5 x$