Question

Solve using inverse operations.

-3/5x=2/5

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve this equation, we need to isolate the variable x. To do this, we can start by multiplying both sides of the equation by the reciprocal of -3/5, which is -5/3. This will cancel out the -3/5 on the left side of the equation:

(-5/3)(-3/5)x = (-5/3)(2/5)

The -3/5 on the left side simplifies to -1, and the equation becomes:

(-5/3)(-1)x = (-5/3)(2/5)

x = (-5/3)(2/5)

Multiplying the numerators and denominators together, we get:

x = -10/15

The fraction -10/15 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 5:

x = (-10/5)/(15/5)

x = -2/3

Therefore, the solution to the equation -3/5x = 2/5 is x = -2/3.

Answer 2

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

To solve the equation -3/5x = 2/5 using inverse operations, we need to isolate the variable x.

First, let's multiply both sides of the equation by the reciprocal of -3/5, which is -5/3. Remember, when we multiply both sides of an equation by the same nonzero number, the equation remains balanced.

(-3/5x) * (-5/3) = (2/5) * (-5/3)

Simplifying both sides, we get:

(3/5) * (5/3) * x = (2/5) * (-5/3)

Now, let's simplify further:

(3 * 5) / (5 * 3) * x = (2 * -5) / (5 * 3)

15/15 * x = -10/15

Since 15/15 is equal to 1, we have:

1 * x = -10/15

Which simplifies to:

x = -10/15

Finally, we can simplify the fraction -10/15 by dividing both the numerator and denominator by their greatest common divisor. The greatest common divisor of 10 and 15 is 5.

(-10/5) ÷ (15/5) = -2/3

Therefore, the solution to the equation -3/5x = 2/5 is x = -2/3.

Answer 3

[AI-generated answer — Explain Bot]

To solve the equation -3/5x = 2/5 using inverse operations, we want to isolate the variable x, which means we want to get x by itself on one side of the equation.

To eliminate the fraction, we can multiply both sides of the equation by 5, which is the reciprocal of 1/5.

(-3/5x)(5) = (2/5)(5)

On the left side, the 5s cancel out, leaving:

-3x = 2

Now, to isolate x, we need to get rid of the coefficient in front of x, which is -3. To do this, we divide both sides of the equation by -3.

(-3x)/(-3) = 2/(-3)

The -3s on the left side cancel out, leaving:

x = -2/3

Therefore, the solution to the equation -3/5x = 2/5 is x = -2/3.