Question

select all of the equations below that are equivalent to 13 - u = 10

13 - u - 4 = 6
13 - u - 7 = 3
13 - u - 2 = 7
13 - u - 7 = 2

Answer 1

To determine which equations are equivalent to the equation \( 13 - u = 10 \), we need to simplify each equation and see if it is true under the same conditions as \( 13 - u = 10 \).

Starting with the original equation:

1. **Original equation:**
\( 13 - u = 10 \)
Rearranging gives:
\( -u = 10 - 13 \)
\( -u = -3 \)
\( u = 3 \)

Now let's check each of the equations given:

1. **Equation 1:**
\( 13 - u - 4 = 6 \)
Simplifying gives:
\( 13 - u = 10 \)
This is equivalent to our original equation.

2. **Equation 2:**
\( 13 - u - 7 = 3 \)
Simplifying gives:
\( 13 - u = 10 \)
This is also equivalent to our original equation.

3. **Equation 3:**
\( 13 - u - 2 = 7 \)
Simplifying gives:
\( 13 - u = 9 \)
This is not equivalent to our original equation.

4. **Equation 4:**
\( 13 - u - 7 = 2 \)
Simplifying gives:
\( 13 - u = 9 \)
This is not equivalent to our original equation.

In summary, the equations that are equivalent to \( 13 - u = 10 \) are:

- \( 13 - u - 4 = 6 \)
- \( 13 - u - 7 = 3 \)

So the equivalent equations are **1 and 2**.