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Chapter 3: Q. 22 (page 171)

In Problems 7鈥�22, solve each inequality.

2(2x2-3x)>-9

Short Answer

Expert verified

The inequality is true on the entire real domain.

Step by step solution

01

Step 1. Given Information

The given inequality is2(2x2-3x)>-9.

02

Step 2. Find the intercepts and vertex

  • Rewrite the inequality in standard form.

4x2-6x+9>0

  • There are no real roots of 4x2-6x+9>0, so, there are no x-intercepts of the curve.
  • The value of f(0)=9.
  • So, the y-intercept is (0,9).
  • Find x=-b2ato find the x - coordinate of the vertex of parabola.

x=68

  • The value of f68=274.
  • So, the vertex is 68,274.
03

Step 3. Graph the Parabola

  • Plot the parabola on a graph by using the obtained intercepts and the vertex.

04

Step 4. Find the region above the x-axis

From the graph, it is observed that the entire curve lies above the x-axis.

So, the entire domain of the function is the solution set.

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