How do you tell if an equation is all real numbers or no solution?

Combine like terms on both sides of the equation. Isolate the x term by subtracting x from both sides. You arrive at the true statement “3 = 3”. When you end up with a true statement like this, it means that the solution to the equation is “all real numbers”.

What does it mean when an equation is true for all values of x?

Any value you choose for x will make the equation a TRUE statement. This type of equation is called an identity, and the solution set is all real numbers. Both sides of the equation represent the same algebraic expression, just written in a different manner.

How do you know when something is all real numbers?

One identifying characteristic of real numbers is that they can be represented over a number line. Think of a horizontal line. The center point, or the origin, is zero. To the right are all positive numbers, and to the left are the negative points.

What does it mean when the solution is all real numbers?

When a true statement such as 0 = 0 results, the equation is an identity, and the solution set is {all real numbers}.

What is an equation that is true for all values of the variable?

An identity is an equation that is true for all possible values of the variable(s) it contains.

How do you know if a function is one-to-one inverse?

A function f(x) has an inverse, or is one-to-one, if and only if the graph y = f(x) passes the horizontal line test. A graph represents a one-to-one function if and only if it passes both the vertical and the horizontal line tests.

What function is not one-to-one?

What Does It Mean if a Function Is Not One to One Function? In a function, if a horizontal line passes through the graph of the function more than once, then the function is not considered as one-to-one function. Also,if the equation of x on solving has more than one answer, then it is not a one to one function.