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Which interval does the inequality (x) 7 define?
The inequality ( x < 7 ) defines the interval ( (-\infty, 7) ). This means that all real numbers less than 7 are included in the solution set, while 7 itself is not included. Conversely, if the inequality were ( x > 7 ), it would define the interval ( (7, \infty) ).
Which values are solutions to the inequality x2 9?
To solve the inequality ( x^2 < 9 ), we first rewrite it as ( x^2 - 9 < 0 ), which factors to ( (x - 3)(x + 3) < 0 ). The critical points are ( x = -3 ) and ( x = 3 ). Analyzing the intervals, we find that the solution to the inequality is ( -3 < x < 3 ). Therefore, the values of ( x ) that satisfy the inequality are those in the open interval ( (-3, 3) ).
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.
How does solving linear inequality differ from solving linear equation?
Linear inequalities are equations, but instead of an equal sign, it has either a greater than, greater than or equal to, less than, or a less than or equal to sign. Both can be graphed. Solving linear equations mainly differs from solving linear inequalities in the form of the solution. 1. Linear equation. For each linear equation in x, there is only one value of x (solution) that makes the equation true. The equation: x - 3 = 7 has one solution, that is x = 10. The equation: 3x + 4 = 13 has one solution that is x = 3. 2. Linear inequality. On the contrary, a linear inequality has an infinity of solutions, meaning there is an infinity of value of x that make the inequality true. All these x values constitute the "solution set" of the inequality. The answers of a linear inequality are expressed in the form of intervals. The linear inequality x + 5 < 9 has as solution: x < 4. The solution set of this inequality is the interval (-infinity, 4) The inequality 4x - 3 > 5 has as solution x > 2. The solution set is the interval (2, +infinity). The intervals can be open, closed, and half closed. The open interval (1, 4) ; the 2 endpoints 1 and 4 are not included in the solution set. The closed interval [-2, 5] ; the 2 end points -2 and 5 are included. The half-closed interval [3, +infinity) ; the end point 3 is included.
When does an inequality have a limited range of solutions?
An inequality has a limited range of solutions when it restricts the values of the variable to a specific interval or set of points. For example, inequalities like ( x < 5 ) or ( 2 < x \leq 7 ) define boundaries that limit the possible values of ( x ). Additionally, inequalities that involve absolute values, such as ( |x - 3| < 2 ), also result in a limited range, as they constrain the variable to fall within a specific distance from a point.
Which interval does the inequality (x) 7 define?
The inequality ( x < 7 ) defines the interval ( (-\infty, 7) ). This means that all real numbers less than 7 are included in the solution set, while 7 itself is not included. Conversely, if the inequality were ( x > 7 ), it would define the interval ( (7, \infty) ).
Which values are solutions to the inequality x2 9?
To solve the inequality ( x^2 < 9 ), we first rewrite it as ( x^2 - 9 < 0 ), which factors to ( (x - 3)(x + 3) < 0 ). The critical points are ( x = -3 ) and ( x = 3 ). Analyzing the intervals, we find that the solution to the inequality is ( -3 < x < 3 ). Therefore, the values of ( x ) that satisfy the inequality are those in the open interval ( (-3, 3) ).
Which expression the inequality x - 2 in interval notation?
x - 2 is not a inequality and so the question does not make any sense.
What is the interval set notation of -7 -3?
-4
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.
How does solving linear inequality differ from solving linear equation?
Linear inequalities are equations, but instead of an equal sign, it has either a greater than, greater than or equal to, less than, or a less than or equal to sign. Both can be graphed. Solving linear equations mainly differs from solving linear inequalities in the form of the solution. 1. Linear equation. For each linear equation in x, there is only one value of x (solution) that makes the equation true. The equation: x - 3 = 7 has one solution, that is x = 10. The equation: 3x + 4 = 13 has one solution that is x = 3. 2. Linear inequality. On the contrary, a linear inequality has an infinity of solutions, meaning there is an infinity of value of x that make the inequality true. All these x values constitute the "solution set" of the inequality. The answers of a linear inequality are expressed in the form of intervals. The linear inequality x + 5 < 9 has as solution: x < 4. The solution set of this inequality is the interval (-infinity, 4) The inequality 4x - 3 > 5 has as solution x > 2. The solution set is the interval (2, +infinity). The intervals can be open, closed, and half closed. The open interval (1, 4) ; the 2 endpoints 1 and 4 are not included in the solution set. The closed interval [-2, 5] ; the 2 end points -2 and 5 are included. The half-closed interval [3, +infinity) ; the end point 3 is included.
When does an inequality have a limited range of solutions?
An inequality has a limited range of solutions when it restricts the values of the variable to a specific interval or set of points. For example, inequalities like ( x < 5 ) or ( 2 < x \leq 7 ) define boundaries that limit the possible values of ( x ). Additionally, inequalities that involve absolute values, such as ( |x - 3| < 2 ), also result in a limited range, as they constrain the variable to fall within a specific distance from a point.
What is the inequality of -2 and 3?
The inequality of -2 and 3 can be expressed as -2 < 3. This indicates that -2 is less than 3 on the number line. In terms of a range, any number greater than -2 and less than 3 can be represented as -2 < x < 3, where x represents any value within that interval.
Which expresses the given inequality in interval notation x less than 4?
The inequality ( x < 4 ) can be expressed in interval notation as ( (-\infty, 4) ). This notation indicates that ( x ) can take any value less than 4, extending infinitely in the negative direction.
What are at least five inequality solutions to x-3?
x - 3 is not an inequality.
Why is it usually only necessary to test one point when graphing an inequality?
One point in each interval. An entire interval, between two critical points, either fulfills, or doesn't fulfill, the inequality.For example, (x-3)(x+5) > 0; the corresponding equality is (x-3)(x+5) = 0, with the two critical points x = 3 and x = -5. The intervals that must be checked are x < -5, x between -5 and 3, and x > 3.
How does solving linear inequalities differ from solving linear equations?
Linear inequalities are equations, but instead of an equal sign, it has either a greater than, greater than or equal to, less than, or a less than or equal to sign. Both can be graphed. Solving linear equations mainly differs from solving linear inequalities in the form of the solution. 1. Linear equation. For each linear equation in x, there is only one value of x (solution) that makes the equation true. Example 1. The equation: x - 3 = 7 has one solution, that is x = 10. Example 2. The equation: 3x + 4 = 13 has one solution that is x = 3. 2. Linear inequality. On the contrary, a linear inequality has an infinity of solutions, meaning there is an infinity of values of x that make the inequality true. All these x values constitute the "solution set" of the inequality. The answers of a linear inequality are expressed in the form of intervals. Example 3. The linear inequality x + 5 < 9 has as solution: x < 4. The solution set of this inequality is the interval (-infinity, 4) Example 4. The inequality 4x - 3 > 5 has as solution x > 2. The solution set is the interval (2, +infinity). The intervals can be open, closed, and half closed. Example: The open interval (1, 4) ; the 2 endpoints 1 and 4 are not included in the solution set. Example: The closed interval [-2, 5] ; the 2 end points -2 and 5 are included. Example : The half-closed interval [3, +infinity) ; the end point 3 is included.
