The questions are illustrations of inequalities
- The solution to the inequality is 7 < x < 11
- The range of the function is (c) R: {f(x) ∈ ℝ | f(x) > 5}
- The solution to the inequality is x < –5 or x > 2
The solution to the inequality
The inequality is given as:
x² - 18x < -77
Add 77 to both sides
x² - 18x + 77 < 0
Expand the inequality
x² - 7x - 11x + 77 < 0
Factorize the inequality
x(x - 7) - 11(x - 7) < 0
Factor out x - 7
(x- 7)(x - 11) < 0
Solve for x
x < 7 or x < 11
This means that the solution to the inequality is 7 < x < 11
The graph that represents the solution
The inequality expression is given as:
y ≤ x² + 2
See attachment for the graph of the inequality
The range of the function
The function is given as:
f(x) = |x| + 5
The smallest value of |x| is 0.
So, we have:
f(x) > 0 + 5
Evaluate
f(x) > 5
Hence, the range of the function is (c) R: {f(x) ∈ ℝ | f(x) > 5}
The solution to the inequality
The inequality expression is given as:
|2x + 3| < 7
Remove the absolute expression
2x + 3 < 7 or 2x + 3 < -7
Subtract 3 from both sides
2x < 4 or 2x < -10
Divide both sides by 2
x < 2 or x < -5
Hence, the solution to the inequality is x < –5 or x > 2
Read more about inequality at:
https://brainly.com/question/11234618
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