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An open statement is a sentence that contains a variable , such as x. The solution set for an open sentence is the set of values that when substituted for the variable make a true statement. The members of the solution set are called solutions. Examples: x = 2. Solution set is {2} solution is 2. x2 - 5 = 4 Solution set is {-3, 3 } solutions are -3 and 3. x > 0 Solution set = {x " x > 0 } That is all positive numbers. Every positive number is a solution. There are some finer points that I did not mention such as the possibility of more than one variable and limitations on the values that allowed in the substitutions.
You must substitute values for the variable.
An expression that contains at least one variable is called an algebraic expression. Algebraic expressions consist of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. These expressions can be simplified or evaluated by substituting specific values for the variables. Algebraic expressions are fundamental in algebra and are used to represent mathematical relationships and solve equations.
They make up the solution set.
A system of equations has an infinite set of solutions when the equations define the same line, such that for ax + by = c, the values for two equations is a1/a2 + b1/b2 = c1/c2. Equations where a variable drops out completely, e.g. 3x - y = 6x -2y there are either an infinite number of solutions, or no solution at all.
When the value of a variable in an algebraic expression changes, the value of the expression can change.
They are identical or equivalent.
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Linear algebraic inequalities can be described as an expression with a variable >/< an expression with a variable. For example, 2x<90 so x<45. Inequalities don't yield a particular solution, but rather solution sets. In the above example, x<45, means that the solution set is all of the values less than 45.
an open sentence can be either true or false, depending on what values are substituted for the variables. A SOLUTION of an open sentence with on variable is a value that makes the sentence true. The solution of the equation x+3=5 is 2. One solution of the inequality x-1>4 is 6, and there are many more solutions. hope this helps
It is the solution; sometimes also called the root.
a variable
An open statement is a sentence that contains a variable , such as x. The solution set for an open sentence is the set of values that when substituted for the variable make a true statement. The members of the solution set are called solutions. Examples: x = 2. Solution set is {2} solution is 2. x2 - 5 = 4 Solution set is {-3, 3 } solutions are -3 and 3. x > 0 Solution set = {x " x > 0 } That is all positive numbers. Every positive number is a solution. There are some finer points that I did not mention such as the possibility of more than one variable and limitations on the values that allowed in the substitutions.
By definition, an identity is true for all values of the variable. So the solution is the whole of the domain.
The solution to an equation consists of the value (or values) of all the variables such that the equation is true when the variable(s) take those values.
An algebraic solution involves using symbols and variables to represent numbers and relationships, allowing for manipulation of equations to find unknown values. In contrast, an arithmetic solution relies on numerical calculations and direct computation without the use of variables. Essentially, algebraic methods provide a more general approach to solving problems, while arithmetic focuses on specific numerical values.
Is the set of all values for the variable that make the equation true.