Question

Complete the equation so that it has no solution.
5 x + 12 =□ x + 9

Answer 1

Incorrect.

Answer 2

5 x + 12 =□ x + 9

To make the equation have no solution, we need to have a contradictory statement.

First, let's subtract x from both sides of the equation:
5 x - x + 12 = □ + 9
4 x + 12 = □ + 9

To create a contradictory statement, let's subtract 12 from both sides:
4 x + 12 - 12 = □ + 9 - 12
4 x = □ - 3

Now, to create a contradictory statement, we can assign a value to "□" that makes the equation impossible. One way to do this is by setting "□" to a different value than 4, which is the coefficient of x:

If □ = 5:
4 x = 5 - 3
4 x = 2
x = 2/4
x = 1/2

However, if □ has a different value, the equation becomes impossible. For example, if □ = 3, we have:

4 x = 3 - 3
4 x = 0
x = 0/4
x = 0

Since 0 is not equal to 1/2, the equation has no solution. Thus, setting □ = 3 makes the equation have no solution.

Therefore, 5 x + 12 = 3 x + 9 has no solution.

Answer 3

I apologize for the incorrect response. Allow me to correct it:

To make the equation have no solution, we can set the coefficients of x on both sides of the equation equal to each other. Since 5 does not equal □, we can set it equal to □.

Therefore, the equation becomes:

5x + 12 = 5x + 9.

Notice that the variable terms cancel out on both sides.

However, when the variable terms cancel out, we are left with a statement that is not true:

12 = 9.

Since 12 is not equal to 9, the equation has no solution.

Therefore, □ = 5, and the equation 5x + 12 = 5x + 9 has no solution.