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Q: Why do we represent the solution to an inequality with a graph on a number line but we don't do the same for the solution to an equation?

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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

The answer, which may not even exist, depends on the inequality. There is, for example, no greatest solution for x > 5.

If your solution comes from an equation, then you simply plot your answer on the number line. If the solution comes from an inequality, you either circle the solution, or color it in, depending on whether your inequality was < or < =. If it is <, then circle your point on the number line, and shade the line for numbers less than your solution. If it is >, circle your point on the number line, and shade the line for the numbers greater than your solution. If it is <=, repeat above, but instead of circling, shade your solution's point as well.

Substitute the number in the equation. If the resulting statement is true the number is a solution to the equation.

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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".

b2.1 is an expression, not an inequality.

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.

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.

any number that makes the inequality true

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.

If A is a number that makes an equation true, then A is a "solution" to the equation.

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.

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