0
To solve the inequality (8x^2 - x < 0), we first factor it as (x(8x - 1) < 0). The critical points are (x = 0) and (x = \frac{1}{8}). Analyzing the sign of the product in the intervals determined by these points, we find that the inequality holds for (0 < x < \frac{1}{8}). Since there are no integer values of (x) in this interval, the number of different integer values of (x) that satisfy the inequality is zero.
What else can I help you with?
How do you determine which constraints are binding?
The values of the variables will satisfy the equality (rather than the inequality) form of the constraint - provided you are not dealing with integer programming.
Which values satisfy the inequality?
To determine which values satisfy a given inequality, you'll need to analyze the inequality itself. Start by isolating the variable on one side, if necessary. Then, test values within the solution interval or use a sign chart to identify the ranges that meet the inequality's condition. If you provide the specific inequality, I can help identify the exact values that satisfy it.
Is all values of the variable that satisfy the inequality?
To determine if all values of a variable satisfy an inequality, you need to analyze the inequality itself. If it is always true (for instance, a statement like (x + 2 > x + 1) is always true), then all values of the variable satisfy it. However, if specific conditions or limits on the variable exist (like (x > 5)), then only those values that meet the conditions are valid solutions. Thus, the answer depends on the specific inequality in question.
Why do the values of n will the product 3n be less than 50?
To find the values of ( n ) for which the product ( 3n ) is less than 50, we can set up the inequality ( 3n < 50 ). Dividing both sides by 3 gives ( n < \frac{50}{3} ), which simplifies to ( n < 16.67 ). Therefore, the integer values of ( n ) that satisfy this inequality are ( n = 0, 1, 2, \ldots, 16 ).
What does solution of an inequality mean in math?
In mathematics, the solution of an inequality refers to the set of values that satisfy the inequality condition. For example, in the inequality (x > 3), any number greater than 3 is considered a solution. These solutions can often be represented on a number line or in interval notation, illustrating all possible values that fulfill the inequality. Essentially, it identifies the range of values for which the inequality holds true.
How do you determine which constraints are binding?
The values of the variables will satisfy the equality (rather than the inequality) form of the constraint - provided you are not dealing with integer programming.
Which values satisfy the inequality?
To determine which values satisfy a given inequality, you'll need to analyze the inequality itself. Start by isolating the variable on one side, if necessary. Then, test values within the solution interval or use a sign chart to identify the ranges that meet the inequality's condition. If you provide the specific inequality, I can help identify the exact values that satisfy it.
Is all values of the variable that satisfy the inequality?
To determine if all values of a variable satisfy an inequality, you need to analyze the inequality itself. If it is always true (for instance, a statement like (x + 2 > x + 1) is always true), then all values of the variable satisfy it. However, if specific conditions or limits on the variable exist (like (x > 5)), then only those values that meet the conditions are valid solutions. Thus, the answer depends on the specific inequality in question.
Why do the values of n will the product 3n be less than 50?
To find the values of ( n ) for which the product ( 3n ) is less than 50, we can set up the inequality ( 3n < 50 ). Dividing both sides by 3 gives ( n < \frac{50}{3} ), which simplifies to ( n < 16.67 ). Therefore, the integer values of ( n ) that satisfy this inequality are ( n = 0, 1, 2, \ldots, 16 ).
What does solution of an inequality mean in math?
In mathematics, the solution of an inequality refers to the set of values that satisfy the inequality condition. For example, in the inequality (x > 3), any number greater than 3 is considered a solution. These solutions can often be represented on a number line or in interval notation, illustrating all possible values that fulfill the inequality. Essentially, it identifies the range of values for which the inequality holds true.
The values or set of values that makes an inequality or equation true are the?
The values or set of values that make an inequality or equation true are called solutions or roots. In the case of equations, these values satisfy the equation when substituted into it, while for inequalities, they make the inequality hold true. Finding these solutions is a fundamental aspect of algebra and helps in understanding the relationships between variables.
What is the set of all numbers that make the inequality true?
The set of all numbers that make an inequality true is known as the solution set. It consists of all the values of the variable that satisfy the given inequality. This set can be expressed using interval notation or set builder notation, depending on the context of the problem. The solution set is crucial in determining the range of values that satisfy the given conditions.
What are the largest values to an inequality?
The largest values in an inequality refer to the upper limits that satisfy the conditions of that inequality. For example, in the inequality (x < 5), the largest value that (x) can take is just below 5, such as 4.999. In cases of non-strict inequalities, like (x \leq 5), the largest value is exactly 5. Understanding these values is crucial for solving and graphing inequalities.
Find all integer values of x that make the equation or inequality true x2 equals 9?
that would be limited to 3 and -3 for values of x
A quantity that can be equal to any integer and can take any different integer values is known as?
Integer variables
How do tell the solution of an inequality?
Substitute the values of the variables into the inequality. If the inequality is true then they are a solution, if not, they are not.Substitute the values of the variables into the inequality. If the inequality is true then they are a solution, if not, they are not.Substitute the values of the variables into the inequality. If the inequality is true then they are a solution, if not, they are not.Substitute the values of the variables into the inequality. If the inequality is true then they are a solution, if not, they are not.
How do solutions differ for an equation and an inequality both algebraically and graphically?
Algebraically, solutions to an equation yield specific values that satisfy the equality, while solutions to an inequality provide a range of values that satisfy the condition (e.g., greater than or less than). Graphically, an equation is represented by a distinct curve or line where points satisfy the equality, whereas an inequality is represented by a shaded region that indicates all points satisfying the inequality, often including a boundary line that can be either solid (for ≤ or ≥) or dashed (for < or >). This distinction highlights the difference in the nature of solutions: precise for equations and broad for inequalities.
