Question

The equation 4/5x−5=14 is solved as follows. Enter the correct numbers to complete the solution.(2 points) 4/5x−5=1/4 4/5x= Add 5 to both sides of the equation. If the number is an improper fraction, enter the improper fraction. x= Divide both sides of the equation by 4/5 . If the number is an improper fraction, enter the improper fraction.

Answer 1

Let's solve the equation step by step and fill in the missing numbers.

1. Start with the original equation: \[ \frac{4}{5}x - 5 = 14 \]

2. Add 5 to both sides of the equation: \[ \frac{4}{5}x = 14 + 5 \] \[ \frac{4}{5}x = 19 \]

3. Now, divide both sides of the equation by \(\frac{4}{5}\): \[ x = \frac{19}{\frac{4}{5}} \]

   To divide by a fraction, we multiply by its reciprocal: \[ x = 19 \cdot \frac{5}{4} \] \[ x = \frac{95}{4} \]

Now we can fill in the solutions:

• The equation was transformed to: \[ \frac{4}{5}x = 19 \]

• Next, we divided both sides by \(\frac{4}{5}\): \[ x = \frac{95}{4} \]

So the completed solution is:

1. \( \frac{4}{5}x = 19 \)
2. \( x = \frac{95}{4} \)