Problem: What should be added to the twice the rational number -7/4 to get 4/7?

Solution:

To solve this problem, we need to follow the steps given below:

1. Find twice the rational number -7/4.
2. Add an unknown value x to twice the rational number -7/4.
3. Set the resulting expression equal to the given value 4/7.
4. Solve for the unknown value x.

Let's apply these steps one by one.

1. Find twice the rational number -7/4.

Twice the rational number -7/4 can be found by multiplying it by 2:

2 x (-7/4) = -14/4 = -7/2

2. Add an unknown value x to twice the rational number -7/4.

We are asked to add an unknown value x to twice the rational number -7/4. So, the expression becomes:

-7/2 + x

3. Set the resulting expression equal to the given value 4/7.

Now, we have:

-7/2 + x = 4/7

4. Solve for the unknown value x.

To solve for x, we need to isolate it on one side of the equation. We can do this by adding 7/2 to both sides of the equation:

-7/2 + x + 7/2 = 4/7 + 7/2

Simplifying the right-hand side:

-7/2 + x + 7/2 = 57/14

Combining like terms on the left-hand side:

x = 57/14 + 7/2

Finding a common denominator and adding the fractions on the right-hand side:

x = (57/14) + (49/14) = 106/14 = 53/7

Therefore, the value that should be added to the twice the rational number -7/4 to get 4/7 is 53/7.

11/28