(x-1)(x+6) 0 Number Line

3 min read Jun 17, 2024

Solving (x-1)(x+6) = 0 on a Number Line

This article will guide you through solving the inequality (x-1)(x+6) = 0 and representing the solution on a number line.

Understanding the Equation

The equation (x-1)(x+6) = 0 is a quadratic equation in factored form. To find the solutions, we use the Zero Product Property:

If the product of two or more factors is zero, then at least one of the factors must be zero.

Finding the Solutions

Set each factor equal to zero:
- x - 1 = 0
- x + 6 = 0
Solve for x:
- x = 1
- x = -6

Therefore, the solutions to the equation (x-1)(x+6) = 0 are x = 1 and x = -6.

Representing the Solution on a Number Line

Draw a number line: Label the number line with the solutions we found, -6 and 1.
Mark the solutions: Place a solid dot at each point representing the solutions, -6 and 1.
Test intervals: Since the equation is equal to zero, the solution is represented by the points -6 and 1. We do not need to consider intervals between these points.

The number line will have two solid dots, one at -6 and one at 1, indicating that the solutions are the points themselves.

Conclusion

We have successfully solved the equation (x-1)(x+6) = 0 and represented the solution on a number line. The solutions to the equation are x = 1 and x = -6, which are marked on the number line.