Q: What is the difference between algebraic solution and graphical solution to an equation?

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In algebraic terms, the solution is the answer to equation.

No. That is because 2 - 8x is an algebraic expression, not an equation. And since it is not an equation, it does not have a solution.

If I understand the question correctly, it is when the algebraic equation (or inequality) is true.

It is the solution or root of the equation.

The graphical method is often approximate but can be applied to any function. If done on a computer, the region surrounding the solution can be enlarged to obtain more accurate estimates. A numerical method will give an exact result is an analytical solution is possible. If not, the solution will depend on the numerical method used and, sometimes, the starting "guesstimate".

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In algebraic terms, the solution is the answer to equation.

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.

You get the exact solution.

A solution is the answer to an equation.

No. That is because 2 - 8x is an algebraic expression, not an equation. And since it is not an equation, it does not have a solution.

If I understand the question correctly, it is when the algebraic equation (or inequality) is true.

It is the solution or root of the equation.

The graphical method is often approximate but can be applied to any function. If done on a computer, the region surrounding the solution can be enlarged to obtain more accurate estimates. A numerical method will give an exact result is an analytical solution is possible. If not, the solution will depend on the numerical method used and, sometimes, the starting "guesstimate".

An equation can lead to a solution.

That is an algebraic equation. If you are asking what the solution is for the above equation, it would be:d = 7

Root means solution in this context.