Which Number Line Shows Solutions to -2|x| = -6?
When faced with an equation like -2|x| = -6, it can be daunting to determine the solutions without a clear strategy. However, by breaking down the equation and utilizing a number line, we can easily visualize and identify the solutions. In this article, we will analyze the equation -2|x| = -6 and determine the solutions on the number line.
Analyzing the Equation: -2|x| = -6
To begin with, let’s break down the equation -2|x| = -6. The absolute value symbols around x indicate that the value inside them can be either positive or negative. In this case, we are looking for the values of x that satisfy the equation. By dividing both sides of the equation by -2, we get |x| = 3. This means that x could be either 3 or -3 to satisfy the equation.
Now, let’s consider the implications of the absolute value function. The absolute value of a number is always positive, so when we have |x| = 3, we are essentially looking for the numbers that are 3 units away from zero on the number line. In this case, those numbers are 3 and -3. Therefore, the solutions to the equation -2|x| = -6 are x = 3 and x = -3.
Determining the Solutions on the Number Line
To visualize the solutions on the number line, we can plot the points x = 3 and x = -3. Starting from zero, we move three units to the right to represent x = 3 and three units to the left to represent x = -3. Both of these points satisfy the equation -2|x| = -6, as they are 3 units away from zero and result in -6 when substituted back into the equation.
By representing the solutions on the number line, we can clearly see that the values of x that satisfy the equation -2|x| = -6 are 3 and -3. This visual representation not only helps us understand the solutions more intuitively but also allows us to easily identify the correct values of x that make the equation true. Understanding how to analyze equations and determine solutions on the number line is a valuable skill that can simplify complex problems and improve mathematical proficiency.
In conclusion, by analyzing the equation -2|x| = -6 and determining the solutions on the number line, we can effectively solve for the values of x that satisfy the equation. By breaking down the equation and visualizing the solutions, we can gain a deeper understanding of mathematical concepts and improve problem-solving skills. Utilizing the number line as a tool to represent solutions can simplify complex equations and make the process more manageable. Next time you encounter a similar equation, remember to analyze it step by step and utilize the number line to determine the solutions accurately.
