What is the solution of the equation 2/5x+4=1/5 ?(1 point)

Question

Responses

−19/2
negative Start Fraction 19 over 2 End Fraction

−38/25
negative Start Fraction 38 over 25 End Fraction

21/2
Start Fraction 21 over 2 End Fraction

−2/19
negative Start Fraction 2 over 19 End Fraction
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Answer 1

To solve the equation $\frac{2}{5}x+4=\frac{1}{5}$, follow these steps:

1. Isolate the $x$ term: Subtract 4 from both sides: $$\frac{2}{5}x+4-4=\frac{1}{5}-4$$ This simplifies to: $$\frac{2}{5}x=\frac{1}{5}-4$$

2. Convert 4 to a fraction with a common denominator: Since 4 can be expressed as $\frac{20}{5}$: $$\frac{2}{5}x=\frac{1}{5}-\frac{20}{5}=\frac{1-20}{5}=\frac{-19}{5}$$

3. Solve for $x$: Multiply both sides by the reciprocal of $\frac{2}{5}$, which is $\frac{5}{2}$: $$x=\frac{-19}{5}\times \frac{5}{2}$$

4. Simplify: $$x=\frac{-19\cdot 5}{5\cdot 2}=\frac{-19}{2}$$

Thus, the solution to the equation $\frac{2}{5}x+4=\frac{1}{5}$ is $$\boxed{{\displaystyle -\frac{19}{2}}}$$