Question

The equation 4/5x−5=1/4 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

To solve the equation \( \frac{4}{5}x - 5 = \frac{1}{4} \), we start by isolating \( x \).

1. Add 5 to both sides of the equation: \[ \frac{4}{5}x - 5 + 5 = \frac{1}{4} + 5 \] This simplifies to: \[ \frac{4}{5}x = \frac{1}{4} + 5 \]

   To add \( 5 \) to \( \frac{1}{4} \), we convert \( 5 \) into a fraction with a denominator of \( 4 \): \[ 5 = \frac{20}{4} \] So, \[ \frac{1}{4} + \frac{20}{4} = \frac{21}{4} \]

   Thus, we have: \[ \frac{4}{5}x = \frac{21}{4} \]

2. Now divide both sides of the equation by \( \frac{4}{5} \): \[ x = \frac{21}{4} \div \frac{4}{5} \] Dividing by a fraction is the same as multiplying by its reciprocal, so we can rewrite this as: \[ x = \frac{21}{4} \cdot \frac{5}{4} \] This can be computed as: \[ x = \frac{21 \cdot 5}{4 \cdot 4} = \frac{105}{16} \]

Putting this all together, the completed solution looks like:

1. \( \frac{4}{5}x - 5 = \frac{1}{4} \)
2. \( \frac{4}{5}x = \frac{21}{4} \)
3. \( x = \frac{105}{16} \)

So, the correct numbers to complete the solution are:

• For the addition: \( \frac{21}{4} \)
• For the division: \( \frac{105}{16} \)