Determine the missing value that would make this equation have zero solutions.
2 (6x + 7) = 3x +___x + 14
To find the missing value that would make the equation have zero solutions, we need to set the equation equal to 0 and solve for x.
2(6x + 7) = 3x +___x + 14
12x + 14 = 3x + ___x + 14
Combine like terms:
12x = 3x + ___x
We can see that for there to be zero solutions, the coefficient of x on the left side (12x) must be different from the combined coefficient of x on the right side (3x + ___x). In other words, the coefficient of x on the right side must be -12x.
Therefore, the missing value is -12.
thats wrong
Apologies for the incorrect response. Let's try solving the equation correctly:
2(6x + 7) = 3x + ___x + 14
Expand the left side of the equation:
12x + 14 = 3x + ___x + 14
Combine like terms:
12x = 3x + ___x
To make the equation have zero solutions, we need the coefficient of x on the left side (12x) to be equal to the combined coefficient of x on the right side (3x + ___x). In other words, the missing value for the equation to have zero solutions is -3.
Therefore, the correct missing value is -3.
Determine the missing values that would make this equation have infinite solutions.
2 (6x + 7) = 3x +___x +___
To find the missing values that would make the equation have infinite solutions, we need the coefficients of x on both sides of the equation to be equal.
2(6x + 7) = 3x +___x +___
Expanding the left side, we get:
12x + 14 = 3x +___x +___
Combining like terms, we have:
12x = 3x + ___x + ___
To have infinite solutions, the coefficient of x on the left side (12x) must be equal to the combined coefficient of x on the right side (3x + ___x). Similarly, the missing values must be such that when added to 3x, they give us a total of 12x.
Since we want the equation to have infinite solutions, any value for the missing coefficients would work as long as they sum up to 12. For example, we can choose -9 and -3, so that:
12x = 3x + (-9)x + (-3)x
12x = 12x
This equation would have an infinite number of solutions.
Therefore, the missing values that would make this equation have infinite solutions are -9 and -3.
To determine the missing value that would make the equation have zero solutions, we need to find the value that would make the equation contradict itself or become inconsistent.
Let's simplify the equation first:
2(6x + 7) = 3x + ___x + 14
Expanding the brackets:
12x + 14 = 3x + ___x + 14
Combining like terms:
12x = 3x + ___x
To have zero solutions, the coefficients of x on both sides of the equation need to be the same. Since we have 12x on the left side, the missing value must make the right side also have 12x. Thus, the missing value is 9x, making the equation:
12x = 3x + 9x
Now the equation becomes:
12x = 12x
Since the coefficients are the same, the equation is consistent and will have infinite solutions, not zero solutions. Therefore, there is no missing value that would make this equation have zero solutions.
To determine the missing value that would make this equation have zero solutions, we need to set up the equation and solve for the missing value. Here's how:
Given equation: 2(6x + 7) = 3x + ___x + 14
Step 1: Distribute the 2 on the left side of the equation to remove the parentheses:
12x + 14 = 3x + ___x + 14
Step 2: Simplify the equation by combining like terms:
12x + 14 = 4x + ___x + 14
Step 3: Subtract 4x from both sides of the equation to isolate the missing term:
12x - 4x + 14 = ___x + 14
Step 4: Subtract 14 from both sides of the equation:
12x - 4x + 14 - 14 = ___x + 14 - 14
Simplifying further, we get:
8x = ___x
At this point, we can see that the missing value that would make this equation have zero solutions is any value other than 8. If the missing value were 8, the equation would become:
8(8) = 8
This equation would be true, resulting in infinitely many solutions rather than zero solutions. Therefore, any value for the missing term other than 8 would make the equation have zero solutions.