Question

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.

Answer 1

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.

Answer 2

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

Answer 3

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