Solve the absolute value equation. |10x - 1| - 1 = 18 Select the correct choice below, and fill in the answer box if necessary.
OA x = __ (Use a comma to separate answers as needed.)
OB. There are no solutions.
First, let's isolate the absolute value term by adding 1 to both sides of the equation:
|10x - 1| = 19
Now we can split the equation into two cases:
Case 1: 10x - 1 = 19
Solve for x:
10x = 20
x = 2
Case 2: -(10x - 1) = 19
Solve for x:
-10x + 1 = 19
-10x = 18
x = -18/10
x = -9/5
So the solutions to the equation are x = 2 and x = -9/5.
Therefore, the correct choice is:
OA x = 2,-9/5
To solve the absolute value equation |10x - 1| - 1 = 18, we can isolate the absolute value term and then split the equation into two cases.
Case 1: 10x - 1 is positive
In this case, the equation becomes: 10x - 1 - 1 = 18
Simplifying: 10x - 2 = 18
Adding 2 to both sides: 10x = 20
Dividing both sides by 10: x = 2
Case 2: 10x - 1 is negative
In this case, the equation becomes: -(10x - 1) - 1 = 18
Simplifying: -10x + 1 - 1 = 18
Simplifying further: -10x = 18
Dividing both sides by -10: x = -1.8
So the solutions to the equation |10x - 1| - 1 = 18 are x = 2 and x = -1.8.
OA x = 2, -1.8
To solve the absolute value equation |10x - 1| - 1 = 18, we will need to isolate the absolute value expression and then remove the absolute value.
Step 1: Add 1 to both sides of the equation.
|10x - 1| = 19
Step 2: Split the equation into two separate equations to account for the positive and negative cases of the absolute value.
For the positive case:
10x - 1 = 19
For the negative case:
-(10x - 1) = 19
Distribute the negative sign:
-10x + 1 = 19
Step 3: Solve each equation separately.
For the positive case:
add 1 to both sides:
10x = 20
divide both sides by 10:
x = 2
For the negative case:
add 1 to both sides:
-10x = 18
divide both sides by -10:
x = -1.8
The solutions to the absolute value equation are x = 2 and x = -1.8.
Therefore, the correct choice is:
OA x = 2, -1.8