Final answer:
To create an equation with the solution x = -3, we substituted x = -3 into the given expression and solved for the blank, resulting in the equation 7x - (x - 2) = 2x(26/3 + x).
Step-by-step explanation:
To create an equation with one solution of x = -3, we can start with the given expression and make it equivalent to an equation that we know has x = -3 as a solution. Starting with the expression 7x - (x - 2) = 2x(__ + x), our goal is to find a value to fill in the blank (__) that results in a true statement for x = -3.
To find the missing value, we substitute x = -3 into the equation and simplify:
- 7(-3) - ((-3) - 2) = 2(-3)(__ + (-3))
- -21 - (-5) = -6(__ - 3)
- -16 = -6(__ - 3)
Now divide both sides by -6 to solve for the blank:
- 16/6 = __ - 3
- Add 3 to both sides: 16/6 + 3 = __
- __ = 8/3 + 18/3 = 26/3
Therefore, the filled equation would be:
7x - (x - 2) = 2x(26/3 + x)
This equation now has one solution for x, which is x = -3.