Question

What is the solution of the equation 2/5x+4=1/5 ?(1 point) Responses −19/2 negative Start Fraction 19 over 2 End Fraction 212 Start Fraction 21 over 2 End Fraction −38/25 negative Start Fraction 38 over 25 End Fraction −2/19 negative Start Fraction 2 over 19 End Fraction

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the equation 2/5x + 4 = 1/5, we can first subtract 4 from both sides to isolate the term with x:

2/5x = 1/5 - 4

Simplifying:

2/5x = 1/5 - 20/5

2/5x = -19/5

Next, we can multiply both sides by 5 to get rid of the fraction:

5 * (2/5x) = 5 * (-19/5)

2x = -19

Finally, divide both sides by 2 to solve for x:

x = -19/2

The solution to the equation is x = -19/2. So, the correct response is: −19/2 (negative Start Fraction 19 over 2 End Fraction).

Answer 2

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

To solve the equation 2/5x + 4 = 1/5, you can follow these steps:

Step 1: Subtract 4 from both sides of the equation:
2/5x + 4 - 4 = 1/5 - 4
2/5x = 1/5 - 20/5

Step 2: Simplify the right side of the equation:
2/5x = -19/5

Step 3: To isolate x, multiply both sides of the equation by the reciprocal of 2/5, which is 5/2:
(5/2)(2/5x) = (5/2)(-19/5)
x = -19/2

Therefore, the solution to the equation 2/5x + 4 = 1/5 is x = -19/2.

Answer 3

[AI-generated answer — Explain Bot]

To find the solution to the equation (2/5)x + 4 = 1/5, we need to isolate the variable x. Here's how you can solve it step by step:

Step 1: Subtract 4 from both sides of the equation to isolate the term (2/5)x.
(2/5)x + 4 - 4 = 1/5 - 4

This simplifies to:
(2/5)x = 1/5 - 4

Step 2: Simplify the right-hand side of the equation.
1/5 - 4 can be written as a common fraction:
1/5 = 5/25, so we have:
(2/5)x = 5/25 - 4
(2/5)x = 5/25 - 100/25
(2/5)x = -95/25

Step 3: Now we want to isolate x, so divide both sides of the equation by (2/5).
(2/5)x / (2/5) = (-95/25) / (2/5)

The (2/5) on the left side cancels out, and dividing by (2/5) is equivalent to multiplying by its reciprocal (5/2).
x = (-95/25) * (5/2)
x = (-95 * 5) / (25 * 2)
x = -475 / 50

Step 4: Simplify the expression on the right-hand side.
Divide both the numerator and denominator by the greatest common divisor, which is 25.
x = (-475 ÷ 25) / (50 ÷ 25)
x = (-19) / 2

Therefore, the solution to the equation is x = -19/2.