The solution to the equation is x = -1, and filling in the blanks yields X = -1.
Let's solve the given equation step by step:
4(x + -1/4) + 3 = 5x -(-3)
First, distribute the 4 on the left side:
4x + (-1) + 3 = 5x + 3
Combine like terms:
4x + 2 = 5x + 3
Now, let's isolate the variable x. Subtract 4x from both sides:
2 = x + 3
Subtract 3 from both sides to solve for x:
-1 = x
Now, let's fill in the blanks in the original equation:
4x + ? + 3 = 5x - (-3)
Substitute the value of x into the equation:
4(-1) + ? + 3 = 5(-1) - (-3)
Simplify both sides:
-4 + ? + 3 = -5 + 3
Combine like terms:
-1 + ? = -2
Add 1 to both sides to solve for the blank:
? = -1
So, the completed equation is:
4x + (-1) + 3 = 5x - (-3)
4x - 1 + 3 = 5x + 3