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Q. 19

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Found in: Page 171

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# In Problems 7–22, solve each inequality.$4{x}^{2}+9<6x$

The given inequality has no solution.

See the step by step solution

## Step 1. Given Information

The given inequality is $4{x}^{2}+9<6x$.

## Step 2. Find the Intercepts

• Rewrite the inequality in standard form.

$4{x}^{2}+9-6x<0$

• There are no real roots of $4{x}^{2}+9-6x=0$, so, there are no x-intercepts of the curve.
• The value of $f\left(0\right)=9$.
• So, the y-intercept is $\left(0,9\right)$.
• Find $x=\frac{-b}{2a}$ to find the x - intercept of the vertex of parabola.

$x=\frac{6}{8}$

• The value of $f\left(\frac{6}{8}\right)=\frac{27}{4}$ .
• So, the vertex is $\left(\frac{6}{8},\frac{27}{4}\right)$.

## Step 3. Plot the Graph

• Plot the parabola on a graph using the vertex and intercepts calculated in the previous step.

## Step 4. Find the region below x-axis

• From the graph, there is no region that lies below the x-axis.
• So, the given inequality has no solution.