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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.
When we plot all the points that satisfy an equation or inequality we do what to it?
Graph it (the equation).
What are the characteristics of the graph of the inequality x 4.5?
The graph of the inequality ( x < 4.5 ) is a vertical line drawn at ( x = 4.5 ), with a dashed line indicating that the line itself is not included in the solution set. The region to the left of this line represents all the values of ( x ) that satisfy the inequality. Therefore, the area shaded will extend infinitely to the left, indicating that all ( x ) values less than 4.5 are solutions.
What is the image obtained by plotting all points that satisfy an equation or inequality?
graph
What does it mean to describe all of the numbers that satisfy both inequalities?
I assume you have inequalities that involve variables. If you replace the variable by some number, you will get an inequality that is either true or false. A value for the variable that results in a true statement is said to "satisfy" the inequality. For example, in: x + 3 > 10 If you replace x by 8, you get a true statement, since 11 is greater than 10; if you replace x by 7, you get a false statement, since 10 is not greater than 10. In this case, there are two inequalities; you have to find all numbers that satisfy both inequalities; in other words, that convert both inequalities into true statements.
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 is any and all values of the variable that satisfies an equation inequality system of equations or system of inequalities?
They make up the solution set.
When we plot all the points that satisfy an equation or inequality we it?
graph
When we plot all the points that satisfy an equation or inequality we?
graph
When we plot all the points that satisfy an equation or inequality we do what to it?
Graph it (the equation).
What are the characteristics of the graph of the inequality x 4.5?
The graph of the inequality ( x < 4.5 ) is a vertical line drawn at ( x = 4.5 ), with a dashed line indicating that the line itself is not included in the solution set. The region to the left of this line represents all the values of ( x ) that satisfy the inequality. Therefore, the area shaded will extend infinitely to the left, indicating that all ( x ) values less than 4.5 are solutions.
What is the image obtained by plotting all points that satisfy an equation or inequality?
graph
In the graph of a linear inequality the shaded region above or below the line is called?
The shaded region above or below the line in the graph of a linear inequality is called the solution region. This region represents all the possible values that satisfy the inequality. Points within the shaded region are solutions to the inequality, while points outside the shaded region are not solutions.
Which values from the set 12345 make the inequality true n 26?
To determine which values from the set {1, 2, 3, 4, 5} make the inequality n < 26 true, we need to find all numbers in the set that are less than 26. In this case, the values that satisfy the inequality are 1, 2, 3, 4, and 5. Therefore, the values from the set {1, 2, 3, 4, 5} that make the inequality n < 26 true are 1, 2, 3, 4, and 5.
What does it mean to describe all of the numbers that satisfy both inequalities?
I assume you have inequalities that involve variables. If you replace the variable by some number, you will get an inequality that is either true or false. A value for the variable that results in a true statement is said to "satisfy" the inequality. For example, in: x + 3 > 10 If you replace x by 8, you get a true statement, since 11 is greater than 10; if you replace x by 7, you get a false statement, since 10 is not greater than 10. In this case, there are two inequalities; you have to find all numbers that satisfy both inequalities; in other words, that convert both inequalities into true statements.
What does solving a system of equations actually mean?
That means to find values for all the variables involved, so that they satisfy ALL the equations in a system (= set) of equations.That means to find values for all the variables involved, so that they satisfy ALL the equations in a system (= set) of equations.That means to find values for all the variables involved, so that they satisfy ALL the equations in a system (= set) of equations.That means to find values for all the variables involved, so that they satisfy ALL the equations in a system (= set) of equations.
How can you tell if a table of values represents a function?
If all the values of the "independent" variable (x) are different then it is a function.If there are any repeats of the independent variable, the corresponding dependent variable, y, must be the same.If all the values of the "independent" variable (x) are different then it is a function.If there are any repeats of the independent variable, the corresponding dependent variable, y, must be the same.If all the values of the "independent" variable (x) are different then it is a function.If there are any repeats of the independent variable, the corresponding dependent variable, y, must be the same.If all the values of the "independent" variable (x) are different then it is a function.If there are any repeats of the independent variable, the corresponding dependent variable, y, must be the same.
