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The equation 4/5x−5=1/4

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.

3 answers

To solve the equation \( \frac{4}{5}x - 5 = \frac{1}{4} \), we can proceed step by step:

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

  2. Add 5 to both sides of the equation. First, let's express 5 as a fraction with a denominator of 4: \[ 5 = \frac{20}{4} \]

    Now, add \( \frac{20}{4} \) to both sides: \[ \frac{4}{5}x = \frac{1}{4} + \frac{20}{4} \] \[ \frac{4}{5}x = \frac{21}{4} \]

  3. Now let's divide both sides of the equation by \( \frac{4}{5} \): \[ x = \frac{21}{4} \div \frac{4}{5} \]

    To divide by a fraction, multiply by its reciprocal: \[ x = \frac{21}{4} \times \frac{5}{4} = \frac{21 \cdot 5}{4 \cdot 4} = \frac{105}{16} \]

Now we can summarize the steps:

  1. The equation \( \frac{4}{5}x = \frac{21}{4} \).
  2. The solution for \( x \) is \( x = \frac{105}{16} \).

Thus, the filled values are:

  • \( \frac{4}{5}x = \frac{21}{4} \)
  • \( x = \frac{105}{16} \)
The equation −2.4x−1.1=3.7
is solved as follows. Enter the correct numbers to complete the solution.(1 point)
−2.4x−1.1=3.7

−2.4x=

Add 1.1 to both sides of the equation. If the answer is a decimal value, enter the decimal.

x=

Divide both sides of the equation by -2.4. If the answer is a decimal value, enter the decimal.

To solve the equation \( -2.4x - 1.1 = 3.7 \), we can follow these steps:

  1. Start with the original equation: \[ -2.4x - 1.1 = 3.7 \]

  2. Add \( 1.1 \) to both sides of the equation: \[ -2.4x = 3.7 + 1.1 \] Now, calculate the right side: \[ 3.7 + 1.1 = 4.8 \] So: \[ -2.4x = 4.8 \]

  3. Now divide both sides of the equation by \( -2.4 \): \[ x = \frac{4.8}{-2.4} \] Calculating this gives: \[ x = -2.0 \]

So the filled values are:

  • \( -2.4x = 4.8 \)
  • \( x = -2.0 \)