Marion is solving the equation 9x − 6 = 12 . As a first step, she adds 6 to both sides of the equation. In the next step, by what value does each side need to be divided? (1 point)
In the next step, each side needs to be divided by 9.
In the equation 9x - 6 = 12, Marion adds 6 to both sides of the equation to isolate the variable on one side.
So the equation becomes:
9x = 12 + 6
Next, to isolate the variable x, Marion needs to divide both sides of the equation by 9, since the variable is being multiplied by 9.
So each side needs to be divided by 9.
Therefore, the value by which each side needs to be divided is 9.
To solve the equation 9x - 6 = 12, Marion correctly added 6 to both sides of the equation in the first step. The next step is to isolate the variable x by getting rid of the constant term on the left side.
To do this, we need to undo the subtraction of 6. Since subtraction is the opposite operation of addition, we can cancel it out by performing the opposite operation, which is addition.
Adding 6 to both sides, we get:
9x - 6 + 6 = 12 + 6.
Simplifying this gives us:
9x = 18.
Now, to solve for x, we need to get rid of the coefficient 9 that is multiplying the variable. Since multiplication is the opposite operation of division, we can cancel out the multiplication by dividing both sides of the equation by 9.
Dividing both sides by 9, we get:
(9x)/9 = 18/9.
Simplifying this gives us:
x = 2.
Therefore, each side of the equation needs to be divided by 9 in the next step.