Solve the equation. 2|x - 9| = 10 Select the correct choice and, if necessary, fill in the answer box in your choice below.
O A. x = (Simplify your answer. Use a comma to separate answers as needed.)
OB. There is no solution.
To solve the equation 2|x - 9| = 10, we need to isolate the absolute value term.
Dividing both sides of the equation by 2, we get |x - 9| = 5.
Now, we'll split the equation into two cases, one for the positive and one for the negative:
Case 1: x - 9 is positive.
In this case, the absolute value term becomes x - 9. So we have x - 9 = 5.
Solving for x, we get x = 14.
Case 2: x - 9 is negative.
In this case, the absolute value term becomes -(x - 9), which simplifies to -x + 9. So we have -x + 9 = 5.
Solving for x, we get x = 4.
Therefore, the solutions to the equation 2|x - 9| = 10 are x = 4 and x = 14.
Answer: A. x = 4, 14
To solve the equation 2|x - 9| = 10, we need to isolate the absolute value expression and then solve for x.
Step 1: Divide both sides of the equation by 2: |x - 9| = 5
Step 2: The absolute value equation |x - 9| = 5 can be rewritten as two separate equations:
1) x - 9 = 5
2) -(x - 9) = 5
Step 3: Solve each equation separately:
1) x - 9 = 5
Add 9 to both sides: x - 9 + 9 = 5 + 9
Simplify: x = 14
2) -(x - 9) = 5
Distribute the negative sign: -x + 9 = 5
Subtract 9 from both sides: -x + 9 - 9 = 5 - 9
Simplify: -x = -4
To isolate x, multiply both sides by -1 (to switch the sign):
(-1)(-x) = (-1)(-4)
Simplify: x = 4
Therefore, the solution to the equation 2|x - 9| = 10 is x = 4, 14.
Answer: A. x = 4, 14
To solve the equation 2|x - 9| = 10, we need to isolate the absolute value expression and then solve for x.
Step 1: Divide both sides of the equation by 2 to get rid of the coefficient in front of the absolute value:
|x - 9| = 5
Step 2: Split the equation into two separate cases, one where the expression inside the absolute value is positive, and one where it is negative:
Case 1: x - 9 > 0 --> x > 9
Case 2: x - 9 < 0 --> x < 9
Step 3: Solve each case separately:
Case 1: x - 9 > 0
If x > 9, then the absolute value expression becomes:
x - 9 = 5
Now we can solve for x:
x = 5 + 9
x = 14
Case 2: x - 9 < 0
If x < 9, then the absolute value expression becomes:
-(x - 9) = 5
Simplify the expression by distributing the negative sign:
-x + 9 = 5
Now we can solve for x:
x = 9 - 5
x = 4
So we have two possible solutions: x = 14 and x = 4.
The correct choice is:
O A. x = 14, 4