The equation 45x−5=1/4

Question

is solved as follows. Enter the correct numbers to complete the solution.(1 point)
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 \( 45x - 5 = \frac{1}{4} \), let's follow through the steps and fill in the missing numbers.

1. Start with the original equation: \[ 45x - 5 = \frac{1}{4} \]

2. You have transformed it into: \[ \frac{4}{5}x - 5 = \frac{1}{4} \] This transformation suggests dividing the entire equation by \( \frac{45}{5} = 9 \), so let's work with that first.

3. Now, to isolate \( \frac{4}{5}x \), we need to add 5 to both sides: \[ \frac{4}{5}x = \frac{1}{4} + 5 \]

To add \( 5 \) (which can be expressed as \( \frac{20}{4} \)): \[ \frac{1}{4} + \frac{20}{4} = \frac{21}{4} \]

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

4. Next, we need to solve for \( x \). We divide both sides by \( \frac{4}{5} \): \[ x = \frac{\frac{21}{4}}{\frac{4}{5}} = \frac{21}{4} \cdot \frac{5}{4} = \frac{21 \times 5}{4 \times 4} = \frac{105}{16} \]

Hence, the completed equations are:

• \( \frac{4}{5}x = \frac{21}{4} \)
• \( x = \frac{105}{16} \)

To finalize your answers:

• \( 4/5x = \frac{21}{4} \)
• \( x = \frac{105}{16} \)