How is solving -4x=-4.8 different from solving -1/4x = -4.8? How are the solutions related?
In the first case I would be dividing both sides by -4
In the second equation I would be multiplying both sides by -4
the two answers differ by a factor of 16
To solve the equation -4x = -4.8, the goal is to isolate the variable x. We can do this by dividing both sides of the equation by -4, which gives us:
-4x / -4 = -4.8 / -4
Simplifying further, we have:
x = 1.2
On the other hand, to solve the equation -1/4x = -4.8, we can begin by multiplying both sides of the equation by -4 to eliminate the fraction:
-4 * (-1/4x) = -4 * (-4.8)
This simplifies to:
x = 19.2
So, the solutions for -4x = -4.8 and -1/4x = -4.8 are different. The solution for -4x = -4.8 is x = 1.2, while the solution for -1/4x = -4.8 is x = 19.2. The solutions are related in that they represent the values of x that make each equation true. However, the two equations have different coefficients in front of x, leading to different solutions.
To understand the difference between solving -4x = -4.8 and -1/4x = -4.8, we need to look at the coefficients in front of the variable x.
In -4x = -4.8, the coefficient of x is -4, whereas in -1/4x = -4.8, the coefficient of x is -1/4.
Let's solve each equation step by step and see how the solutions relate to each other:
1. Solving -4x = -4.8:
To isolate x, we divide both sides of the equation by -4 (which is the coefficient of x):
-4x / -4 = -4.8 / -4
x = 1.2
The solution to the equation -4x = -4.8 is x = 1.2.
2. Solving -1/4x = -4.8:
To isolate x, we need to get rid of the coefficient of -1/4. To do this, we multiply both sides of the equation by -4/1, which is the reciprocal of -1/4:
(-1/4x) * (-4/1) = -4.8 * (-4/1)
x = 19.2
The solution to the equation -1/4x = -4.8 is x = 19.2.
The solutions to the two equations are x = 1.2 and x = 19.2, respectively. In terms of their relationship, we can observe that the solutions are reciprocals of each other.
To summarize:
-4x = -4.8 has a solution of x = 1.2.
-1/4x = -4.8 has a solution of x = 19.2.
The solutions are related by the reciprocal property, meaning that if one solution is a, the other solution is 1/a. In this case, 1.2 and 19.2 are reciprocals of each other: 1/1.2 = 19.2 and 1/19.2 = 1.2.