Determine the missing values that would make this equation have infinite amount of solutions
2(6x+7)=3x+?=∆
To have an infinite amount of solutions, the equation must be true for any value of x.
To ensure this, we need to have the equation simplify to an identity.
Starting with the given equation:
2(6x + 7) = 3x + ∆
Expanding the equation:
12x + 14 = 3x + ∆
Simplifying by subtracting 3x from both sides:
9x + 14 = ∆
To make this equation have an infinite amount of solutions, ∆ must be equal to 9x + 14.
Therefore, the missing value that would make the equation have an infinite amount of solutions is ∆ = 9x + 14.
To have an infinite number of solutions, the expression 2(6x+7) must be equal to the expression 3x + ?.
Let's simplify the left side of the equation:
2(6x+7) = 12x + 14
Now, the equation becomes:
12x + 14 = 3x + ?
To have an infinite number of solutions, the two sides of the equation need to be identical. This means that the coefficients of x must be equal and the constants must be equal.
Comparing the coefficients of x:
12x = 3x
To make these coefficients equal, we can set x equal to any value.
Comparing the constants:
14 = ?
To make the constants equal, the missing value should be 14.
Thus, the missing value that would make this equation have an infinite number of solutions is 14.
To determine the missing value that would make the equation have an infinite number of solutions, we need to find a value that, when substituted, results in both sides of the equation being equal.
Let's start by simplifying the equation:
2(6x + 7) = 3x + ?
First, distribute the 2 to each term inside the parentheses:
12x + 14 = 3x + ?
Next, let's isolate the variable terms by subtracting 3x from both sides:
12x - 3x + 14 = ?
Simplifying further:
9x + 14 = ?
To have an infinite number of solutions, the missing value needs to make the equation true regardless of the value of x. In other words, the equation should be true for any x.
In this case, since the equation only contains the variable x and a constant term, there is no missing value that will result in an infinite number of solutions. The equation will only have a single solution for x, not an infinite number.