The equation 4/5x−5=1/4

Question

is solved as follows. Enter the correct numbers to complete the solution.(2 points)
4/5x−5=1/4

45x=

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.

Given the equation: $$\frac{4}{5}x-5=\frac{1}{4}$$

1. Add 5 to both sides: $$\frac{4}{5}x=\frac{1}{4}+5$$

To add $5$, we can convert it to a fraction with a common denominator: $$5=\frac{5\times 4}{1\times 4}=\frac{20}{4}$$

Now we can add: $$\frac{1}{4}+\frac{20}{4}=\frac{21}{4}$$

So we have: $$\frac{4}{5}x=\frac{21}{4}$$

2. Multiply both sides by $5$ to eliminate the fraction in front of $x$: $$4x=\frac{21}{4}\cdot 5$$ $$4x=\frac{21\times 5}{4}=\frac{105}{4}$$

3. Now we can write the equation without fractions as: $$45x=105$$

4. Now, divide both sides by $4$ to solve for $x$: $$x=\frac{105}{4}÷\frac{4}{5}$$

Dividing by a fraction is the same as multiplying by its reciprocal: $$x=\frac{105}{4}\cdot \frac{5}{4}=\frac{105\times 5}{4\times 4}=\frac{525}{16}$$

So the completed solution is:

1. $\frac{4}{5}x=\frac{21}{4}$ (from adding 5)
2. $45x=105$ (when multiplying both sides by $5$)
3. $x=\frac{525}{16}$ (when dividing both sides by $\frac{4}{5}$)