Introduction:

The given equation is ax + b = 0. To find the solution for this equation, we need to isolate the variable x. The solution will provide the value(s) of x that satisfy the equation.

Isolating x:

To isolate x, we need to get rid of the constant term b. We can do this by subtracting b from both sides of the equation:

ax + b - b = 0 - b

This simplifies to:

ax = -b

Dividing by a:

To solve for x, we need to isolate it on one side of the equation. Since x is multiplied by a, we can divide both sides of the equation by a:

ax/a = -b/a

This simplifies to:

x = -b/a

Final Solution:

The solution to the equation ax + b = 0 is x = -b/a. This means that when the value of x is equal to -b/a, the equation will be satisfied.

Example:

Let's take a numerical example to understand this better. Suppose we have the equation 2x + 6 = 0. We can see that a = 2 and b = 6.

Using the formula x = -b/a, we can substitute the values:

x = -6/2

Simplifying this gives:

x = -3

Therefore, the solution to the equation 2x + 6 = 0 is x = -3, which means that when x is equal to -3, the equation is satisfied.

Summary:

In summary, the solution to the equation ax + b = 0 is x = -b/a. By isolating x and dividing by a, we can find the value(s) of x that satisfy the equation. This solution allows us to determine the value of x that makes the equation true.