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The answer depends on the form of the equation and the domain.

For example,

- there is no solution for x + 2 = 0 if the domain is positive integers, but there is if x can be a negative integer.
- there is no solution for 2x = 1 for integer x but there is if x can be a rational number.
- there is no solution for x^2 = 2 for rational x but there is if x can be an irrational number.
- there is no real solution for x^2 = -2 for real x there is if x can be a complex number.

There are many other equations in one variable for which cannot be solved.

However, for simple equations, you may get a solution by making the same changes to both sides of the equation (with some exceptions, like division by zero, or taking square roots, etc) until you rename one side as the variable.

For example, to solve

(2x + 3)/5 = 9

Multiply both sides by 5: 2x + 3 = 45

Subtract 3 from both sides: 2x = 42

Divide both sides by 2: x = 21.

Solution of inequalities is the same except that if you multiply or divide by a negative number then the inequality changes direction.

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Q: How can you solve an equation or inequality in one variable?

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isolate the variable

each of the four regions created on the coordinate plane by the x- and y-axes.

you can only solve for one in an equation so it can equal something

When an equation has a variable in it (only one), then there are only certainvalues the variable can have that will make the equation a true statement."Solving" the equation means finding those values for the variable.

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You can write an equivalent equation from a selected equation in the system of equations to isolate a variable. You can then take that variable and substitute it into the other equations. Then you will have a system of equations with one less equation and one less variable and it will be simpler to solve.

This cannot be solved. Just like an equation, an inequality has to have at least one variable and at least one operator, such as less than, greater than, etc. Yours has no operator. Please restate your question.

The general idea is to solve one of the equations for one variable - in terms of the other variable or variables. Then you can substitute the entire expression into another equation or other equations; as a result, if it works you should end up having one less equation, with one less variable.

Algebraically manipulate the equation until you have the indicated variable on one side of the equation and all of the other factors on the other side.

Assuming the simplest case of two equations in two variable: solve one of the equations for one of the variables. Substitute the value found for the variable in all places in which the variable appears in the second equation. Solve the resulting equation. This will give you the value of one of the variables. Finally, replace this value in one of the original equations, and solve, to find the other variable.

Algebraic Inequality

When you solve a one-variable equation, your goal is to isolate the variable.To isolate the variable means to make it be alone on one side of the equals sign.In the equation shown here, you can isolate the variable by subtracting 9 from both sides of the equation and simplifying

If you're given the inequality and the equation, then the way to prove that they have the same solution is to solve each one and show that the solutions are the same number. Don't strain yourself, though. An inequality and an equation never have the same solution.

algebraic inequality, is an inequality that contains at least one variable.

You use substitution when you can solve for one variable in terms of the others. By substituting, you remove one variable from the equation, which can then be solved. Once you solve for one variable, you can use substitution to find the other.

Your equation has two variables in it ... 'a' and 'x'. So the solution is a four-step process: 1). Get another independent equation that relates the same two variables. 2). Solve one of the equations for one of the variables. 3). Substitute that into the other equation, yielding an equation in a single variable. Solve that one for the single variable. 4). Substitute that value back into the first equation, and solve it for the second variable.

1. Elimination: Select two equations and a variable to eliminate. Multiply each equation by the coefficient if that variable in the other equation. If the signs of the coefficient for that variable in the resulting equations are the same then subtract one new equation from the other. If they have opposite signs then add them. You will now have an equation without that variable. Repeat will other pairs and you will end up with one fewer equation and one fewer variable. Repeat this process: after each round you will have one fewer equation and one fewer variable. Keep going until you are left with one equation in one variable. Solve that. Then work backwards solving for the other variables.2. Substitution: Select a equation and a variable. Make that variable the subject of the equation. The right hand side of this equation is an expression for that variable. Substitute this expression for the variable is each of the other equations. Again, one fewer equation in one fewer variable. Continue until you are left with one equation in one variable. Solve that. Then work backwards solving for the other variables.3. Matrix inversion: If A is the nxn matrix of coefficients, X is the nx1 [column] matrix of variables and B is the nx1 matrix of the equation constants, then X = A^-1*B where A^-1 is the inverse of matrix A.

That's exactly the purpose of the substitution method ... to get an equation with one less variable. When you have it, you solve it for the variable that's left.

An equation or an inequality that contains at least one variable is called an open sentence. ... When you substitute a number for the variable in an open sentence, the resulting statement is either true or false. If the statement is true, the number is a solution to the equation or inequality.

It depends on the specific inequality. In the simplest cases, it is solved just like an equation; except that you must be careful when multiplying and dividing - if you multiply or divide both sides by a negative number, you must switch the inequality sign. For instance, a "less-than" sign would be changed to a "greater-than" sign.

32.5100 has excactly the same value as 32.51

I, for one, am certainly not going to solve that.It is an expression, not an equation nor inequality and expressions cannot be solved.

There are four steps in an algebraic elimination problem. These steps are: to find a variable with equal or opposite coefficients, if equal then subtract the equations but if opposite then add, solve one variable equation left, and then substitute known variable into other equation and solve. hi

It means that you manipulate the equation in such a way that the variable appears only on one side, by itself.

Solve like any other math equation. One thing to remember; if you multiply or divide through by a negative number, reverse the inequality.