Could x = -5 be a solution to the inequality -6 < 3x + 9 < 21?
2 answers:
<em>So you think that x = -5 is the solution for the inequality? Let's check it out.</em>
<em>(Check)</em>
<em>- Substitute x = -5 in the inequality</em>
<em /><em />
<em>If it was the symbol ≤ you'd be correct, but it's < so It's a bit wrong.</em>
<em />
<em>Now let's solve the inequality. Separate the inequality by parts.</em>
<em /><em />
<em>Therefore, the inequality is true only when x > -5 or x < 4.</em>
<em />
<em>(Check)</em>
<em>- Substitute x = -4 in the inequality.</em>
<em /><em />
<em>The inequality is true for first case.</em>
<em>- Substitute x = 3 in the inequality</em>
<em /><em />
<em>The inequality is true for second case.</em>
<em />
<em>So the answer for inequality is -5 < x < 4</em>
<em />
<em>That means only {-4, -3, -2, ..., 3} can make the inequality true.</em>
You might be interested in
<span>Given:
75% of the five-star football recruits in the nation go to universities in the three most competitive athletic conferences. </span>→ 25% goes to other schools.
<span>
five-star recruits get full football scholarships 93% of the time, regardless of which conference they go to. </span>→ 7% of the 5-star recruits don't get full football scholarships.<span>
a. The probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship?
75% * 93% = 69.75%
b. What are the odds a randomly selected five-star recruit will not select a university from one of the three best conferences?
25% of selected five-star recruit will not select a university from one of the three best conferences. I got the number based on the given data. Since, 75% will go, the remaining percent won't go. Total percentage should be 100% of the population.
c. Explain whether these are independent or dependent events. Are they Inclusive or exclusive?
These are independent events. One can still go to different school and still be legible for the full football scholarship.
For question 2, pls. see attachment.</span>
75% of the five-star football recruits in the nation go to universities in the three most competitive athletic conferences. </span>→ 25% goes to other schools.
<span>
five-star recruits get full football scholarships 93% of the time, regardless of which conference they go to. </span>→ 7% of the 5-star recruits don't get full football scholarships.<span>
a. The probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship?
75% * 93% = 69.75%
b. What are the odds a randomly selected five-star recruit will not select a university from one of the three best conferences?
25% of selected five-star recruit will not select a university from one of the three best conferences. I got the number based on the given data. Since, 75% will go, the remaining percent won't go. Total percentage should be 100% of the population.
c. Explain whether these are independent or dependent events. Are they Inclusive or exclusive?
These are independent events. One can still go to different school and still be legible for the full football scholarship.
For question 2, pls. see attachment.</span>
