The given equation has an infinite number of solutions. What must be the missing number or expression?
5(x – 4) + ? = 1 + 12x – 21
A.
7x
B.
8x
C.
20
D.
40
wrong again
don't you even have your NLP routines check their answer?
yeah it's pretty bad for math questions
To solve this equation and find the missing number or expression, we need to simplify the equation by distributing and combining like terms.
Starting with the left side of the equation:
5(x - 4) is equal to 5 times x minus 5 times 4, which simplifies to 5x - 20.
The equation becomes:
5x - 20 + ? = 1 + 12x - 21
Next, combine like terms on both sides of the equation. The constants (-20 and -21) can be combined on the right side, while the variables (5x and 12x) can be combined on the left side:
5x + ? = 1 + 12x - 41
Consolidating the constants on the right side:
5x + ? = 12x - 40
Now, to find the missing number or expression, we need to make the coefficients of the variables on both sides equal. Since the coefficient of x on the left side is 5 and on the right side is 12, we can multiply the left side by 2 to make them equal:
2(5x) + ? = 2(12x) - 40
10x + ? = 24x - 40
Comparing the left and right sides, we can see that the missing expression or number must make the two sides equal. By subtracting 10x from both sides, we get:
? = 24x - 10x - 40
? = 14x - 40
Therefore, the missing number or expression is 14x - 40.
Checking the answer choices:
A. 7x: This is not equivalent to 14x - 40.
B. 8x: This is not equivalent to 14x - 40.
C. 20: This is not equivalent to 14x - 40.
D. 40: This is not equivalent to 14x - 40.
None of the answer choices are correct. The correct missing expression is 14x - 40.