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If you replace the equal sign of an equation an put an inequality sign in its place is there ever a time when the same value will be a solution to both the equation and inequality?
Yes, when the inequality has a less that or equal to sign, or a greater than sign or equal to sign, then the equal sign can be replaced and get a solution that is common to both the equation and the inequality. There can also be other solutions to the inequality, where as the solution for the equation will be a valid one.
If you replace the equal sign of equation with inequality sign is there ever a time when the same value will be a solution to both the equation and the inequality?
No. You have written two quantities. They can't be equal to each other AND also UNequal to each other.
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.
How is an extraneous solution of a ration equation similar to an excluded value of a rational equation?
An extraneous solution of a rational equation is a solution that emerges from the algebraic process but does not satisfy the original equation, while an excluded value is a value that makes the denominator zero and is therefore not permissible in the equation. Both concepts highlight the limitations and constraints of rational expressions. Excluded values can lead to extraneous solutions if they are mistakenly included in the solution set. Thus, both are essential to consider when solving rational equations to ensure valid solutions.
What is the answer called in a equation?
The answer in an equation is called the "solution." It is the value or values that satisfy the equation, making both sides equal when substituted into the expression. In the case of equations with multiple variables, the solution may represent a set of values.
If you replace the equal sign of an equation an put an inequality sign in its place is there ever a time when the same value will be a solution to both the equation and inequality?
Yes, when the inequality has a less that or equal to sign, or a greater than sign or equal to sign, then the equal sign can be replaced and get a solution that is common to both the equation and the inequality. There can also be other solutions to the inequality, where as the solution for the equation will be a valid one.
If you replace the equal sign of an equation and put an inequality sign in its place is there ever a time when the same value will be a solution to both the equation and inequality?
No - It will lead to a contradiction. No - It will lead to a contradiction.
If you replace the equal sign of equation with inequality sign is there ever a time when the same value will be a solution to both the equation and the inequality?
No. You have written two quantities. They can't be equal to each other AND also UNequal to each other.
Is there ever a time when the same value will be a solution for both an equation and an inequality?
See this example: x + 2 ≥ 4 x + 2 - 2 ≥ 4 - 2 x ≥ 2
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.
How is an extraneous solution of a ration equation similar to an excluded value of a rational equation?
An extraneous solution of a rational equation is a solution that emerges from the algebraic process but does not satisfy the original equation, while an excluded value is a value that makes the denominator zero and is therefore not permissible in the equation. Both concepts highlight the limitations and constraints of rational expressions. Excluded values can lead to extraneous solutions if they are mistakenly included in the solution set. Thus, both are essential to consider when solving rational equations to ensure valid solutions.
What is the answer called in a equation?
The answer in an equation is called the "solution." It is the value or values that satisfy the equation, making both sides equal when substituted into the expression. In the case of equations with multiple variables, the solution may represent a set of values.
What is the solution to the inequality x squared 100?
The inequality ( x^2 < 100 ) can be solved by first taking the square root of both sides, giving ( -10 < x < 10 ). Thus, the solution is the interval ( (-10, 10) ). This means that any value of ( x ) within this range will satisfy the inequality.
What does an equation and an inequality have in common?
They both have variables. They both have addition, subtraction, multiplication, and division.
What is a value or values that make an equation true?
A value or values that make an equation true are known as the solutions or roots of the equation. For example, in the equation (x + 3 = 7), the value (x = 4) is a solution because substituting it into the equation balances both sides. In general, solutions satisfy the equality expressed in the equation.
How is a extraneous solution of a ration equation similar to a excluded value of a rational equation?
An extraneous solution of a rational equation is a solution that arises from the algebraic process of solving the equation but does not satisfy the original equation. This can occur when both sides are manipulated in ways that introduce solutions not valid in the original context. An excluded value, on the other hand, refers to specific values of the variable that make the denominator zero, rendering the equation undefined. Both concepts highlight the importance of checking solutions against the original equation to ensure they are valid.
Which will solve N in 8xN plus 40 equals?
Nothing will solve an expression. You need an equation (an equality or an inequality) beofre a solution of any kind is possible. Tha means you need something on both sides of the equality (or inequality) sign.
