When solving an equation, it is important to accurately represent the solutions on a number line. In this article, we will discuss the solutions to the equation |x + 4| = 2, and which number line they would be represented on.
Understanding the Problem
The equation |x + 4| = 2 can be broken down into two separate equations. The first equation is x + 4 = 2, and the second equation is x + 4 = -2. The vertical lines that surround the x in the equation indicate that the equation is an absolute value equation. This means that the solutions are always positive, regardless of the sign of the number inside of the vertical lines.
Analyzing the Solutions
When solving the first equation, x + 4 = 2, the solution can be found by subtracting 4 from both sides. This leaves us with x = -2. This means that the solution to the equation is -2. When solving the second equation, x + 4 = -2, the solution can be found by subtracting 4 from both sides. This leaves us with x = -6. This means that the solution to the equation is -6.
The solutions to the equation |x + 4| = 2 can be represented on a number line by placing a dot at -2 and -6. This means that the number line that represents the solutions to the equation is -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7.
In conclusion, when solving an absolute value equation, it is important to accurately represent the solutions on a number line. The solutions to the equation |x + 4| = 2 can be found by solving the two separate equations, x + 4 = 2 and x + 4 = -2. The solutions can be represented on a number line by placing a dot at -2 and -6.
The number line is a staple of mathematics education, used to explain and illustrate the concepts of negative and positive numbers. Recently, number lines have become popular for illustrating the solutions to equations like |x + 4| = 2. This particular equation can be solved using a number line, and in this article, we will explore the answer the equation provides and how it can be represented on the number line.
At its most basic, the equation |x + 4| = 2 can be read as “the absolute value of x plus four equals two”. To solve it, the absolute value of x can be determined by subtracting four from both sides to get x = -2. This implies that the two solutions of the equation are -2 and +2, representing the positive and negative values of x.
When represented on a number line, these two solutions can be easily identified. Starting from the origin, the point at -2 represents the first solution, while the point at +2 represents the second solution. These points can be joined by a straight line across the number line, showing the two solutions to the equation.
It should be noted that the equation |x + 4| = 2 may also be written as |x – (-4)| = 2, which is the same as |x – 4| = 2. If this variant of the equation is used, the same answer is provided – the two points at +2 and -2 – but when visualizing it on the number line, the solution line must appear slightly differently. In this case, it should begin at the point at -4 on the number line and cross over to +2, indicating the magnitude of the difference between any two numbers on the number line.
In conclusion, the equation |x + 4| = 2 is easily solved using a number line. In this case, the solutions are -2 and +2, indicated by the two points on the number line. If the variant |x – 4| = 2 is used, the solution line should begin from the point at -4 instead. With these visualizations, it is easy to understand the answer the equation provides.
