Question

1.What is the solution of the equation 5/2x = −1/8 ?(1 point)

2.What is the solution of the equation −x/2.9=−3 ?(1 point)Responses

3.What is the solution of the equation 8/5x = −10 ?(1 point)Responses

Answer 1

[AI-generated answer — Bot GPT 3.5]

1. To solve the equation 5/2x = -1/8, we can cross-multiply.

Multiplying both sides by 2 and then dividing by 5, we have:
x = (-1/8) * (2/5)
x = -1/20

2. To solve the equation -x/2.9 = -3, we can multiply both sides by 2.9 to eliminate the fraction.
Multiplying both sides by 2.9, we have:
(-x/2.9) * 2.9 = -3 * 2.9
-x = -8.7
Dividing both sides by -1, we have:
x = 8.7

3. To solve the equation 8/5x = -10, we can cross-multiply.
Multiplying both sides by 5, we have:
(8/5x) * 5 = -10 * 5
8 = -50x
Dividing both sides by -50, we have:
x = 8/-50
x = -0.16 or -1/6

Answer 2

[AI-generated answer — Step-by-Step Bot]

1. To solve the equation 5/2x = -1/8, we can start by multiplying both sides of the equation by the reciprocal of 5/2, which is 2/5. This will eliminate the fraction on the left side.

(5/2x) * (2/5) = (-1/8) * (2/5)

Canceling out the common factors, we have:

(1x) = (-1/4)

Simplifying further, we get:

x = -1/4

So, the solution to the equation is x = -1/4.

2. To solve the equation -x/2.9 = -3, we can start by multiplying both sides of the equation by the reciprocal of -1/2.9, which is -2.9. This will eliminate the fraction on the left side.

(-x/2.9) * (-2.9) = (-3) * (-2.9)

Canceling out the common factors, we have:

(-1x) = (8.7)

Simplifying further, we get:

x = -8.7

So, the solution to the equation is x = -8.7.

3. To solve the equation 8/5x = -10, we can start by multiplying both sides of the equation by the reciprocal of 8/5, which is 5/8. This will eliminate the fraction on the left side.

(8/5x) * (5/8) = (-10) * (5/8)

Canceling out the common factors, we have:

(1x) = (-50/8)

To simplify this further, we can divide the numerator and denominator of the fraction by their greatest common factor, which is 2:

x = (-25/4)

So, the solution to the equation is x = -25/4.

Answer 3

[AI-generated answer — Explain Bot]

To find the solution for these equations, we can use a process called "solving for x." Let's go through each equation step-by-step to find the solution.

1. The equation is 5/2x = -1/8.
To start, we want to get rid of the fraction on the left side of the equation. We can do this by multiplying both sides of the equation by the reciprocal of the fraction, which is -8/1.
Multiplying -8/1 to both sides, we get: (-8/1)(5/2)x = (-8/1)(-1/8)
This simplifies to: -20x/2 = 1/8
Now, on the left side, we can divide both sides by -20/2 to isolate the variable x.
Dividing -20x/2 by -20/2, we get: x = (1/8)(-2/20)
Simplifying this further, we have x = -1/80.
Therefore, the solution to this equation is x = -1/80.

2. The equation is -x/2.9 = -3.
Similar to the previous equation, let's begin by getting rid of the fraction on the left side of the equation. We can do this by multiplying both sides of the equation by the reciprocal of the fraction, which is 2.9/(-1).
Multiplying 2.9/(-1) to both sides, we get: (2.9/(-1))(-x/2.9) = (2.9/(-1))(-3)
This simplifies to: x = 8.7.
Therefore, the solution to this equation is x = 8.7.

3. The equation is 8/5x = -10.
Once again, let's start by getting rid of the fraction on the left side of the equation. We can do this by multiplying both sides of the equation by the reciprocal of the fraction, which is 5/8.
Multiplying 5/8 to both sides, we get: (5/8)(8/5x) = (5/8)(-10)
This simplifies to: x = -25.
Therefore, the solution to this equation is x = -25.

Keep in mind that these are just the steps to solve these specific equations. The process may differ for different types of equations.