Solve the equation. 2|5y - 6| - 5 = 7 Select the correct choice and, if necessary, fill in the answer box in your choice below.
O A. y = (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) OB. There is no solution.
To solve the equation, we need to isolate the absolute value term.
First, let's add 5 to both sides of the equation:
2|5y - 6| - 5 + 5 = 7 + 5
2|5y - 6| = 12
Now, divide both sides of the equation by 2:
(2/2)|5y - 6| = 12/2
|5y - 6| = 6
To remove the absolute value, we can set up two separate equations, one for the positive value inside the absolute value and one for the negative value inside the absolute value.
1) 5y - 6 = 6
2) 5y - 6 = -6
For equation 1, add 6 to both sides:
5y - 6 + 6 = 6 + 6
5y = 12
Now divide both sides by 5:
(5/5)y = 12/5
y = 12/5
For equation 2, add 6 to both sides:
5y - 6 + 6 = -6 + 6
5y = 0
Now divide both sides by 5:
(5/5)y = 0/5
y = 0
So the solutions to the equation are y = 12/5 or y = 0.
The correct choice is:
A. y = 12/5, 0
To solve the equation, we will isolate the absolute value expression and then solve for y.
Step 1: Add 5 to both sides of the equation to isolate the absolute value expression:
2|5y - 6| = 12
Step 2: Divide both sides of the equation by 2:
|5y - 6| = 6
Step 3: Write two separate equations for the positive and negative forms of the absolute value:
5y - 6 = 6 and -(5y - 6) = 6
Step 4: Solve each equation separately:
For 5y - 6 = 6:
Add 6 to both sides:
5y = 12
Divide both sides by 5:
y = 12/5
For -(5y - 6) = 6:
Distribute the negative sign to both terms inside the absolute value:
-5y + 6 = 6
Subtract 6 from both sides:
-5y = 0
Divide both sides by -5:
y = 0
Therefore, the correct choice is:
O A. y = 12/5, 0
To solve the equation 2|5y - 6| - 5 = 7, we need to isolate the absolute value term and then solve for y. Here's how you can do it:
1. Add 5 to both sides of the equation:
2|5y - 6| = 12
2. Divide both sides of the equation by 2:
|5y - 6| = 6
Now, we have two cases to consider:
Case 1: (5y - 6) is positive:
5y - 6 = 6
Add 6 to both sides of the equation:
5y = 12
Divide both sides of the equation by 5:
y = 12/5
Case 2: (5y - 6) is negative:
-(5y - 6) = 6
Remove the negative sign by multiplying both sides of the equation by -1:
5y - 6 = -6
Add 6 to both sides of the equation:
5y = 0
Divide both sides of the equation by 5:
y = 0
The two possible solutions for y are y = 12/5 and y = 0. Therefore, the correct choice is:
O A. y = 12/5, 0