Determine the missing values that would make this equation have infinite amount of solutions. Both answers will be integers.2(6x+7)=−4x+ _ x+_
To have an infinite number of solutions, the equation should be true regardless of the values of x. Therefore, the coefficients of x on both sides of the equation should be equal.
In the given equation, the coefficient of x on the left side is 12 (2 multiplied by 6), and on the right side, it is -4.
To make them equal, we can choose any two integers that satisfy the equation 12 = -4.
One possible choice could be x = -3.
Now, let's substitute x = -3 into the original equation and find the missing values:
2(6x + 7) = -4x + _x + _
2(6(-3) + 7) = -4(-3) + _(-3) + _
2(-18 + 7) = 12 + _ + _
2(-11) = 12 + _ + _
-22 = 12 + _ + _
To make the equation true, the missing values could be any pair of integers that add up to -34. For example, one possible solution is:
-22 = 12 - 23 + (-11)
To determine the missing values that would make the equation have an infinite amount of solutions, we need to examine the equation and understand its properties. In this case, we have the equation:
2(6x + 7) = -4x + _x + _
To begin, let's simplify the equation by distributing the 2 on the left side:
12x + 14 = -4x + _x + _
Next, let's combine like terms on both sides of the equation:
12x + 14 = -4x + _x + _
To make this equation have an infinite number of solutions, we need the x terms on both sides of the equation to cancel each other out (i.e., their coefficients should be the same). In this case, we have -4x and _x.
To make -4x + _x = 0 (or cancel each other out), the coefficient of -4x must be the same as the coefficient of _x, but with opposite signs (one positive and one negative).
Thus, the missing values that will give an infinite number of solutions are the same numerical value but with opposite signs. For example, if the missing value is 3, it should be replaced with -3.
Therefore, the missing values in this equation that would make it have an infinite number of solutions are any opposite integer values, such as -3 and 3.
To have an infinite amount of solutions, the equation must be true for any value of x. This means the coefficients of x on both sides of the equation must cancel out.
In the given equation, we have:
2(6x + 7) = -4x + mx + nx
Expanding the left side of the equation:
12x + 14 = -4x + mx + nx
For the x terms to cancel out, the coefficient of x on the right side (-4x + mx + nx) must be equal to the coefficient of x on the left side (12x).
This means:
-4 + m + n = 12
To have an infinite amount of solutions, any values for m and n can be chosen as long as their sum equals 16.
For example, one possible solution is:
m = 9
n = 7
Thus, the missing values that would make this equation have an infinite amount of solutions are:
-4x + 9x + 7x