Difference between revisions of "1962 AHSME Problems/Problem 29"
(Created page with "==Problem== Which of the following sets of x-values satisfy the inequality 2x^2 + x < 6? <math> \textbf{(A)}\ -2 < x <\frac{3}{2}\qquad\textbf{(B)}\ x >\frac{3}2\text{ or }x <-...") |
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==Problem== | ==Problem== | ||
| − | Which of the following sets of x-values satisfy the inequality 2x^2 + x < 6? | + | Which of the following sets of <math>x</math>-values satisfy the inequality <math>2x^2 + x < 6</math>? |
<math> \textbf{(A)}\ -2 < x <\frac{3}{2}\qquad\textbf{(B)}\ x >\frac{3}2\text{ or }x <-2\qquad\textbf{(C)}\ x <\frac{3}2\qquad</math> | <math> \textbf{(A)}\ -2 < x <\frac{3}{2}\qquad\textbf{(B)}\ x >\frac{3}2\text{ or }x <-2\qquad\textbf{(C)}\ x <\frac{3}2\qquad</math> | ||
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==Solution== | ==Solution== | ||
| − | + | First, subtract 6 from both sides of the inequality, | |
| + | <math>2x^2 + x - 6 < 0</math>. | ||
| + | This is a parabola that opens upward when graphed, it has a positive leading coefficient. So any negative x values must be between its x-axis intersections, namely <math>x = -2, 1.5</math>. The answer is A. | ||
Latest revision as of 21:23, 4 June 2018
Problem
Which of the following sets of 
-values satisfy the inequality 
?
Solution
First, subtract 6 from both sides of the inequality,
.
This is a parabola that opens upward when graphed, it has a positive leading coefficient. So any negative x values must be between its x-axis intersections, namely 
. The answer is A.
