The equation 4/5x−5=1/4

is solved as follows. Enter the correct numbers to complete the solution.(1 point)
45x−5=14

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.

1 answer

Let's solve the equation step by step and fill in the blanks with the correct numbers.

Given equation: \[ \frac{4}{5}x - 5 = \frac{1}{4} \]

Step 1: Add 5 to both sides of the equation

To isolate the term with \(x\), we need to add \(5\) to both sides.

Adding \(5\) (which can be written as \(\frac{20}{4}\) for common denominators), we have: \[ \frac{4}{5}x = \frac{1}{4} + 5 \]

Calculating the right side: \[ 5 = \frac{20}{4} \]

Now add: \[ \frac{1}{4} + \frac{20}{4} = \frac{21}{4} \]

Thus, the equation is: \[ \frac{4}{5}x = \frac{21}{4} \]

Step 2: Solve for \(x\)

To find \(x\), we will multiply both sides by the reciprocal of \(\frac{4}{5}\), which is \(\frac{5}{4}\): \[ x = \frac{21}{4} \cdot \frac{5}{4} \]

Calculating the right side gives: \[ x = \frac{21 \cdot 5}{4 \cdot 4} = \frac{105}{16} \]

Filling in the blanks:

  1. From \(\frac{4}{5}x = \frac{21}{4}\), we note that the answer to the first blank is: \[ \frac{21}{4} \]

  2. For \(x\), we found: \[ x = \frac{105}{16} \]

Final Answers:

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