Determine the missing coefficient of x that would make this equation have infinite solutions. 2(24x+7)=39x+ x+14
To have infinite solutions, the coefficient of x in both sides of the equation must be equal. Therefore, we need to find the missing coefficient of x on the right side of the equation.
On the left side, we have 2(24x+7), which can be simplified to 48x+14.
On the right side, we have 39x+x+14, which can be simplified to 40x+14.
To make the equation have infinite solutions, we need the coefficient of x on both sides to be equal. Therefore, we need the missing coefficient of x to be 48.
To determine the missing coefficient of x that would make the equation have infinite solutions, we need to equate the coefficients of x on both sides of the equation.
On the left side of the equation, we have 2 multiplied by the expression (24x + 7), which equals 48x + 14.
On the right side of the equation, we have 39x + x + 14, which simplifies to 40x + 14.
Now we equate the coefficients of x:
48x + 14 = 40x + 14
By subtracting 40x from both sides of the equation:
8x + 14 = 14
To find the missing coefficient of x, we need to eliminate the variable term on the left side of the equation. We can do this by subtracting 14 from both sides:
8x = 0
Dividing both sides of the equation by 8:
x = 0
So, the missing coefficient of x that would make the equation have infinite solutions is 0.
To determine the missing coefficient of x that would make the equation have infinite solutions, we need to set up an equation and solve for the missing coefficient.
Let's rewrite the given equation:
2(24x + 7) = 39x + x + 14
To begin, we distribute the 2 to both terms inside the parentheses:
48x + 14 = 39x + x + 14
Next, we combine like terms on both sides of the equation:
48x + 14 = 40x + 14
Now, we subtract 40x from both sides to isolate the variable:
8x + 14 = 14
To solve for x, we subtract 14 from both sides:
8x = 0
Finally, we divide both sides by 8 to find the value of x:
x = 0
Since we have found a specific value for x (x = 0), this equation does not have infinite solutions. Therefore, there is no missing coefficient that would make it have infinite solutions.