Math and Arithmetic

Algebra

Calculus

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In a nonlinear equation, each variable must only have one solution.

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0undefined means you can not do the operation (5/0 is undefined) no solution refers to an equation not having an answer. a solution is a number which you can plug into the variable of an equation and get a true statement. So having no solution means there is no number which you can plug in and get a true statement. As a fraction is not an equation, but an expression it is not right to say that 5/0 has no solution. There is no variable in 5/0, nothing to plug into to get a true or false statement.

I'm going to assume you have an equation to go with your variable? It means "Check if this number works" What to do is put the given value into the equation instead of the variable and see if the result is true - if it is you have a solution, if not you don't. I'll make one up as a demo: Equation : a + 4 = 7 is a = 2 a solution? a+4=7 2+4=7 6=7 (FALSE!) No this given value is not a solution.

A linear equation in one variable. Case 1: A conditional equation: True only for a value of the variable. Ex. x + 2 = 3, True only when x is 1. Case 2: Identity Equation: Always true. Ex. x + 2 = x + 2, True for any value of x. Case 3: x + 1 = x + 5, False for any value of x. We call a solution any value of the variable that satisfies the equation, meaning if we replace the variable with that value, the equation becomes a true statement. Example: -2(x -3) = 8 - 2x -2x + 6 = 8 - 2x (add 2x and subtract 6 to both sides) 0 = 2 False. Since this equation, which is equivalent to the original equation, is false, then the original equation is also false. Meaning, there is no real number for x that could satisfy the equation. So there is no solution to the equation.

In math, that refers to an equation which includes a variable. Such an equation may be true, or false, depending on the value assigned to the variable.

A solution to an question makes the equation true. For example a solution to the equation 3x = x + 6 is x = 3, since 3(3) = 3+6.

When an equation is based on false assumptions, you know that it has not solution. At other times, you may be able to tell through trying to solve the equation and constantly failing.

You normally "solve" something when there is a variable involved. In this case there is no variable. All you have to do is decide whether it is true or false. If this is derived from an original equation (or, in this case, inequality) which involved variables, then if the equation (or inequality) without variables is true, it means it is true for ANY value of the variable. If it is false, the original equation (or inequality) can't be satisfied by any value of the variable.

21 is the only solution of that equation.

You substitute the coordinates of the point in the equation. If the result is true then the point is a solution and if it is false it is not a solution.

You replace the variable by the number, do all specified calculations, and then check whether the resulting inequality is true or false. This is basically not very different from checking a solution of an equation.

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

the answer is false - apex

False, think of each linear equation as the graph of the line. Then the unique solution (one solution) would be the intersection of the two lines.

By solving the equation. If you get some contradictory equation, the original equation has no solution, assuming you did everything correctly. For example, if you solve:x + 3 = x + 2 by subtracting x on both sides, you get: 3 = 2 which is always false (regardless of the value of "x").

There is no simple way which can be easily applied to all forms of equations. If the variable(s) can be eliminated from the equation then, if what is left isfalse, then the equation has no solution.true, then the equation is an identity.The problem is complicated by the domains under consideration. The following are some examples of equations which have no solutions in one domain but do in another [larger] domain:x + 2 = 0 has no solution in N (natural numbers) but does in Z (integers)x*2 = 1 has no solution in Z but does in Q (rational numbers)X^2 = 2 has no solution in Q but does in R (real numbers)x^2 = - 2 has no solution in R but does in C (complex numbers).

If you use a variable, or variables, with an equation, or with an inequality, it is neither true nor false until you replace the variables with specific values.

An equation can have zero solutions, one solution, two solutions, or many solutions. A solution is any number that, when replaced into the equation, will give an equality. An example of an equation without a solution is x = x + 1. No matter what number you use for "x", the right part will always be one more than the left part. Therefore, the equation has no solution. (Also, if you subtract "x" from each side, you get the equation 0 = 1, which is obviously false.)

There can be no solution to an algebra equation because of limitations of the domain. For example,x+3 = 2 has no solution if the domain for x is the set of positive integers,x*3 = 2 has no solution if the domain for x is the set of whole numbers,x^3 = 2 has no solution if the domain for x is the set of rational numbers,x^2 = -2 has no solution if the domain for x is the set of real numbers.Alternatively, the equation has no solution if it can be reduced to a false statement. For example,x + 2 = x + 3 can be simplified to 2 = 3 which is false and so there is no solution.

An equation is a statement. If it includes a variable, then it's only true for certain values of the variable and false for all others, and to "solve" it means to find those values. An equation without variables is also a statement. Either the statement is true or else it isn't. If the statement isn't true, then it's not an equation. Either way, it was nice of someone to hand it to you, but there's nothing that needs to be done with it. It asks no question, poses no problem, and seeks no solution.

Answer: no solution3x - 2 = 3x -53x - 3x - 2 = 3x - 3x - 5 (Subtract 3x from each side.)-2 = -5 Huh??When you are solving an equation, and the variable disappears, there are two possibilities:If you are left with a true statement (such as 2 = 2), then the equation is an identity, and any value of x will satisfy the equation. The number of solutions is infinite.If you are left with a false statement, as in this case, no value of x will satisfy the equation. There is no solution.

Every sentence to which standard logic applies has exactly one of the truth values (that is, either true or false, but not both). No sentence can be both true and false.An equation is a statement that sets two mathematical expressions equal.When both sides of an equation are numerical expressions (contain no variables), the equation is a closed statement. This means the equation can be assigned a truth value.Example:2 + 5 = 7 true 2(3) - 2 = 6 falseIf an equation is neither true nor false, the equation is an open sentence.An open sentence is a mathematical statement with one or more variables. When variables are present in an equation, the solution is unknown. The set of numbers that you use to represent the variable(s) is called the replacement set. The solution set is found when any value(s) for the variable from the replacement set makes the equation a true statement.Examples: 3x+6=20; 12n-5=45; 6a+2b+7c=84; 4p>25; 9s+24To solve one you have to find the value of the variable.If an equation is true for all values of the variables involved, then it is called an identity. For example 4(x -3) = 4x - 12.If an equation is true only for some values, then it is called a conditional equation. For example, x^2 - 3x - 4 = 0 is only true when x = -1 or x = 4, which are called the roots of thereby emile lefer a 10 year old

3 + 4 = 9 is not an expression, it is an equation (which happens to be false). An equation without a variable is simply a statement which is either true (a tautology) or false. It's main use is probably at the end of a proof where you may show that the left hand side of some equation is numerically the same as the right hand side which proves your proposition. n + 4 = 9 is also not an expression, but an equation. An equation with a variable can divide the domain into distinct partitions such that the equation is true if the value of the variable is within those partitions and not if they are outside. This may enable you to derive further information about he variable(s).

(2, 3) is a solution only if it satisfies the equation. x + 5y = 4 (2) + 5(3) =? 4 2 + 15 =? 4 17 = 4 False Therefore, (2, 3) is not a solution to the given equation.

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