The equation 4/5x−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

Let's solve the equation step by step.

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

Step 1: Add 5 to both sides.

To isolate the term with \( x \), we add \( 5 \) to both sides: \[ \frac{4}{5}x = \frac{1}{4} + 5 \]

To add \( 5 \), we convert it to a fraction. Since \( 5 = \frac{5 \times 4}{4} = \frac{20}{4} \), we have: \[ \frac{1}{4} + \frac{20}{4} = \frac{21}{4} \]

So now we have: \[ \frac{4}{5}x = \frac{21}{4} \]

Step 2: Divide both sides by \( \frac{4}{5} \).

To solve for \( x \), we divide both sides by \( \frac{4}{5} \): \[ x = \frac{\frac{21}{4}}{\frac{4}{5}} \]

Dividing by a fraction is the same as multiplying by its reciprocal: \[ x = \frac{21}{4} \times \frac{5}{4} = \frac{21 \times 5}{4 \times 4} = \frac{105}{16} \]

Putting it all together, we get:

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

So the final answers are:

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

Answer 2

so its, 4/5x = 21/4 and x = 105/16?

Answer 3

Yes, that's correct!

The completed solution is:

• From \( \frac{4}{5}x - 5 = \frac{1}{4} \), after adding 5 to both sides, we have: \[ \frac{4}{5}x = \frac{21}{4} \]

• Then, solving for \( x \) by dividing both sides by \( \frac{4}{5} \): \[ x = \frac{105}{16} \]

So your final answers are:

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

Well done!

Answer 4

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 5

Let's solve the equation step by step.

Starting with the equation: \[ -2.4x - 1.1 = 3.7 \]

Step 1: Add 1.1 to both sides.

To isolate the term with \( x \), we add \( 1.1 \) to both sides: \[ -2.4x = 3.7 + 1.1 \]

Calculating the right side: \[ 3.7 + 1.1 = 4.8 \]

So now we have: \[ -2.4x = 4.8 \]

Step 2: Divide both sides by -2.4.

To solve for \( x \), we divide both sides by \( -2.4 \): \[ x = \frac{4.8}{-2.4} \] Calculating this gives: \[ x = -2 \]

Putting it all together, we get:

1. \( -2.4x = 4.8 \)
2. \( x = -2 \)

So the final answers are:

• For \( -2.4x = \): \( 4.8 \)
• For \( x = \): \( -2 \)