An equation has an equal sign, which means that we know what the variable is equal to :)
We identify a set of points in the relevant space which are part of the solution set of the equation or inequality. The space may have any number of dimensions, the solution set may be contiguous or in discrete "blobs".
any number that makes the inequality true
Substitute the number in the equation. If the resulting statement is true the number is a solution to the equation.
The answer, which may not even exist, depends on the inequality. There is, for example, no greatest solution for x > 5.
The solution set is the answers that make an equation true. So I would call it the solution.
An algebraic equation or inequality can have a solution, an algebraic expression cannot. If substituting a number in place of a variable results in the equation or inequality being a true statement, then that number is a solution of the equation or inequality.
solution set
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.
If I understand the question correctly, it is when the algebraic equation (or inequality) is true.
We identify a set of points in the relevant space which are part of the solution set of the equation or inequality. The space may have any number of dimensions, the solution set may be contiguous or in discrete "blobs".
Answer 1 == In an open sentence (an equation or inequality with a variable in it), when a number replacing the variable makes the sentence true, then it is a solution.
A number is an expression. It is not an equation, or an inequality, since it doesn't have an equal sign, or an inequality (greater than, less than, etc.) sign.
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.
b2.1 is an expression, not an inequality.
any number that makes the inequality true
No, inequalities have more than, less then, at least, or no more than signs. Equations just have equal signs. An inequality answer can't be written as just a number it has to have a sign with it.
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.