#3 ### Inequalities and Graphing Relations**3. Solve the following inequalities and represent the solution in interval notation. Show your work!****(a) \(6x^2 - 4 \geq 5x + 2\)****(b) \(x|x - 4| < 3\)****4. Sketch the graph of the relation \(R = \{(x, y) \mid x^2 - 2x - 2 \leq y \leq 2x - x^2 + 2\}\).**### Instructions for Students:1. **Solving Inequalities:** - For each inequality, isolate the variable \(x\) and determine the solution set. - Convert the solution set into interval notation, which is a way of writing subsets of the real number line.2. **Graphing the Relation:** - Identify the boundaries defined by the inequalities. - Draw the graphs of these boundary equations on a coordinate plane. - Shade the region that represents the solution to the inequalities.### Detailed Graph Explanation:In problem 4, you will be plotting two quadratic functions to determine the region where the inequalities hold:- The first boundary is \(y = x^2 - 2x - 2\). - This is a parabola opening upwards.- The second boundary is \(y = 2x - x^2 + 2\). - This is a parabola opening downwards.### Steps to Graph:1. **Find Vertex and Intercepts:** - Determine the vertex of each parabola. - Find the x-intercepts by solving \(x^2 - 2x - 2 = 0\) and \(2x - x^2 + 2 = 0\).2. **Plot Points:** - Plot the vertex and intercept points on a graph. - Draw the parabolas using these points.3. **Shading the Region:** - Identify the region between these two curves. - Shade the area where the inequality \(x^2 - 2x - 2 \leq y \leq 2x - x^2 + 2\) holds.By following these steps, you will understand how to solve inequalities and represent them graphically, a crucial skill in algebra and calculus.

Name: #3 ### Inequalities and Graphing Relations**3. Solve the following ine
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: #3 ### Inequalities and Graphing Relations**3. Solve the following inequalities and represent the solution in interval notation. Show your work!****(a) \(6x^2 - 4 \geq 5x + 2\)****(b) \(x|x - 4| < 3\)****4. Sketch the graph of the relation \(R = \{(x