Which number line represents the solutions to x 5 1 – Which number line represents the solutions to x – 5 = 1? This equation, when graphed on a number line, yields a clear visual representation of its solutions. By understanding the relationship between the equation and the number line, we can effectively solve similar equations and apply this knowledge to real-world scenarios.
To determine the solutions to x – 5 = 1, we employ algebraic methods. By isolating the variable x on one side of the equation, we can identify the value that satisfies the equation. This value, when plotted on the number line, represents the solution to the equation.
Number Line Representation: Which Number Line Represents The Solutions To X 5 1
The equation x – 5 = 1 can be represented on a number line to visualize the solutions. Start by plotting the number 5 on the number line. Since the equation subtracts 5, move 5 units to the right to find the solution.
The solution to the equation is the point where the number line ends after this movement, which is 6.
Solution Set
The solution to the equation x – 5 = 1 is x = 6. This can be determined algebraically by isolating the variable x on one side of the equation. Add 5 to both sides of the equation:
x
5 + 5 = 1 + 5
x = 6
Equation Analysis, Which number line represents the solutions to x 5 1
The equation x – 5 = 1 is a linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 1 and the y-intercept is -5. The solution to the equation is the x-coordinate of the point where the line y = x – 5 intersects the x-axis (y = 0). This point is (6, 0), which confirms the solution x = 6.
Real-World Applications
Understanding the solutions to x – 5 = 1 can be useful in various real-world scenarios, such as:
- Distance calculation:If you travel 5 miles and then continue traveling 1 mile further, the total distance traveled is x – 5 + 1 = 6 miles.
- Time calculation:If you start working at 9 AM and work for 5 hours, the time you finish working is x – 5 + 1 = 3 PM.
Extensions
The concept of number line representation can be extended to solve more complex equations and inequalities, such as:
- Solving 2x- 5 = 1: This equation can be represented on a number line by first plotting 5/2 and then moving 2 units to the right. The solution is x = 3.
- Solving the inequality x- 5 > 1: This inequality can be represented on a number line by shading the region to the right of the point 6.
General Inquiries
What is the solution to x- 5 = 1?
The solution to x – 5 = 1 is x = 6.
How can I use a number line to solve x- 5 = 1?
Start at 5 on the number line and move 1 unit to the right. This will give you the solution, which is 6.
