Open Middle®
Directions: Write three equations whose solution is x = 3.
Hint
What makes a solution equal to 3? What other operations could you use?
Answer
There are an infinite number of equations of varying complexity, as long as the solution is 3.
Source: Dan Meyer
An easy way to get linear equations in one variable with solution 3 is:
Choose any real numbers a and b. Then the following equations will have x = 3 as the solution:
x + a = 3 + a
x – a = 3 – a
ax = 3a
a/x = 3/a
ax + b = 3a + b
And of course all the equations that are equivalent to these, like
a + x = 3 + a (changing the order)
xa – 3a = 0 (rearranging the equation)
ca + cx = 3c + ac (multiplying the whole equation with some c in R)
a + x + c = 3 + a + c (adding a constant c in R on both sides)