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To find the least possible integer solution of the inequality (4.10 < 3x < 19.86), we first solve for (x) by dividing the entire inequality by 3. This gives us (1.3667 < x < 6.62). The least integer greater than (1.3667) is (2). Therefore, the least possible integer solution is (2).
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What is the greatest possible integer solution of the inequality 8.904x 18.037?
To solve the inequality ( 8.904x < 18.037 ), we first isolate ( x ) by dividing both sides by 8.904. This gives us ( x < \frac{18.037}{8.904} ), which approximately equals 2.022. The greatest possible integer solution is therefore ( x = 2 ).
What are the integer solutions of the inequality x 3?
The inequality ( x^3 < 3 ) can be solved by finding the integer values of ( x ) that satisfy this condition. To do this, we first note that ( x^3 = 3 ) has a real solution at ( x = \sqrt[3]{3} \approx 1.442 ). The integer solutions for the inequality ( x^3 < 3 ) are thus ( x = -2, -1, 0, 1 ). Therefore, the integer solutions are ( x \in {-2, -1, 0, 1} ).
What happens to the inequality sign when you divide by a negative integer?
When you divide or multiply both sides of an inequality by a negative integer, the inequality sign must be reversed. For example, if you have the inequality (a < b) and you divide both sides by a negative number, the resulting inequality will be (a / (-n) > b / (-n)), where (n) is a positive integer. This reversal is necessary to maintain the truth of the inequality.
How do you find the integer solution of the inequality x 2?
To find the integer solutions of the inequality ( x^2 < n ) (where ( n ) is a positive integer), first determine the square root of ( n ). The integer solutions for ( x ) will be all integers satisfying ( -\sqrt{n} < x < \sqrt{n} ). This means you consider all integers from ( -\lfloor \sqrt{n} \rfloor ) to ( \lfloor \sqrt{n} \rfloor ), excluding the endpoints if ( n ) is a perfect square.
Which is the smallest integer that makes this inequality 2x 35 true?
To solve the inequality (2x < 35), we first divide both sides by 2, resulting in (x < 17.5). The smallest integer that satisfies this inequality is 17. Therefore, the answer is 17.
What is the greatest possible integer solution of the inequality 8.904x 18.037?
To solve the inequality ( 8.904x < 18.037 ), we first isolate ( x ) by dividing both sides by 8.904. This gives us ( x < \frac{18.037}{8.904} ), which approximately equals 2.022. The greatest possible integer solution is therefore ( x = 2 ).
What are the integer solutions of the inequality x 3?
The inequality ( x^3 < 3 ) can be solved by finding the integer values of ( x ) that satisfy this condition. To do this, we first note that ( x^3 = 3 ) has a real solution at ( x = \sqrt[3]{3} \approx 1.442 ). The integer solutions for the inequality ( x^3 < 3 ) are thus ( x = -2, -1, 0, 1 ). Therefore, the integer solutions are ( x \in {-2, -1, 0, 1} ).
What is the smallest integer solution of 17?
17 is not an equation and so there can be no "solution of 17". There is, therefore, no possible answer to the question.
What happens to the inequality sign when you divide by a negative integer?
When you divide or multiply both sides of an inequality by a negative integer, the inequality sign must be reversed. For example, if you have the inequality (a < b) and you divide both sides by a negative number, the resulting inequality will be (a / (-n) > b / (-n)), where (n) is a positive integer. This reversal is necessary to maintain the truth of the inequality.
How do you find the integer solution of the inequality x 2?
To find the integer solutions of the inequality ( x^2 < n ) (where ( n ) is a positive integer), first determine the square root of ( n ). The integer solutions for ( x ) will be all integers satisfying ( -\sqrt{n} < x < \sqrt{n} ). This means you consider all integers from ( -\lfloor \sqrt{n} \rfloor ) to ( \lfloor \sqrt{n} \rfloor ), excluding the endpoints if ( n ) is a perfect square.
Which is the smallest integer that makes this inequality 2x 35 true?
To solve the inequality (2x < 35), we first divide both sides by 2, resulting in (x < 17.5). The smallest integer that satisfies this inequality is 17. Therefore, the answer is 17.
Which lists all the integer solutions of the inequality of 3?
The question cannot be answered since it contains no inequality.
What are the integer solutions of the inequality x 4?
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Will an equation with an integer coefficient always have an integer solution?
No, an equation with integer coefficients does not always have an integer solution. For example, the equation (x + 1 = 2) has an integer solution, (x = 1), but the equation (2x + 3 = 1) has no integer solution since (x = -1) is not an integer. Solutions depend on the specific equation and its constraints, and rational or real solutions may exist instead.
Does an equation with an integer coefficient always have an integer solution?
No, an equation with integer coefficients does not always have an integer solution. For example, the equation (2x + 3 = 5) has the integer solution (x = 1), but the equation (x^2 + 1 = 0) has no real solutions, let alone integer ones. The existence of integer solutions depends on the specific form and constraints of the equation.
What is integer programming?
Integer programming is a special kind of an optimising problem where the solution must be an integer.
Which lists all the integer solutions of the inequality x 3?
The inequality ( x < 3 ) includes all integer solutions that are less than 3. Therefore, the integer solutions are ( \ldots, -2, -1, 0, 1, 2 ). In interval notation, this can be expressed as ( (-\infty, 3) ) for the integers.
