Solve (using any method), write your answer in interval notation and graph the solution set.
1a. x^2-6>-5x
1b. 6x^2-5x+1
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1a. x^2-6>-5x
1b. 6x^2-5x+1
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1a) The roots of the corresponding equation are 1 and -6. Therefore, the solution to your inequality is
(-inf, -6) U ( 1,inf)
1b) Similarly, the solutions to the second are 1/2 and 1/3. In this case the solution to the inequality is
[1/3,1/2].
- Note the different kind of brackets in 1a and 1b.
- Also note that in the fist case the solution is outside the roots, whereas in the second between the roots of the equation. This is determined by the sign of x^2
Best,
(-inf, -6) U ( 1,inf)
1b) Similarly, the solutions to the second are 1/2 and 1/3. In this case the solution to the inequality is
[1/3,1/2].
- Note the different kind of brackets in 1a and 1b.
- Also note that in the fist case the solution is outside the roots, whereas in the second between the roots of the equation. This is determined by the sign of x^2
Best,
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a. x^2 + 5x - 6 > 0
( x+6) (x - 1) > 0
(-infinity, -6) U ( 1,+infinity) answer
b. 6x^2-5x+1
(3x -1) (2x - 1) < or = 0
[1/3, 1/2] answer
( x+6) (x - 1) > 0
(-infinity, -6) U ( 1,+infinity) answer
b. 6x^2-5x+1
[1/3, 1/2] answer
1
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