Concept explainers
To calculate: The value of x for the inequality 2x2−6x−9≥11 using a table.
The solution of the inequality is (−∞,−2]∪[5,∞) .
Given information:
The inequality is 2x2−6x−9≥11 .
Formula used:
Substitute the values for x into the inequality.
Calculation:
Write the given inequality:
2x2−6x−9≥11
Subtract 11 from both sides to make the right side of the inequality equal to 0,
2x2−6x−9−11≥11−112x2−6x−20≥0x2−3x−10≥0
Substitute the x=−4 in the inequality,
(−4)2−3(−4)−10≥016+12−10≥018≥0
Substitute the x=−3 in the inequality,
(−3)2−3(−3)−10≥09+9−10≥08≥0
Substitute the x=−2 in the inequality,
(−2)2−3(−2)−10≥04+6−10≥00≥0
Similarly make a table by substituting the values of x in the inequality:
x | −4 | −3 | −2 | −1 | 0 | 1 | 2 | 3 | 4 | 5 |
x2−2x−8 | 18 | 8 | 0 | −6 | −10 | −12 | −12 | −10 | −6 | 0 |
The inequality 2x2−6x−9≥11 fails between −2 and 6 and true for all real numbers.
Therefore, (−∞,−2]∪[5,∞) is the solutions for the inequality 2x2−6x−9≥11 .
Chapter 1 Solutions
Algebra 2: New York Edition (holt Mcdougal Larson Algebra 2)
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