The absolute value of (three x plus five) equals twelve x plus 8.
What is being asked in the problem and what does that mean? What plan am I going to try?
Then, solve.
The problem is asking us to find the value of "x" that satisfies the equation involving absolute value.
To solve this problem, we can use the definition of absolute value. The absolute value of a number is equal to the number itself if it is positive or zero, and the negative of the number if it is negative. In this case, we have the absolute value of (three x plus five), which means we need to consider both positive and negative values of (three x plus five).
1. We start by setting (three x plus five) equal to the positive value of twelve x plus 8:
(three x + 5) = 12 x + 8
2. Solve the equation for x:
3x - 12x = 8 - 5
-9x = 3
x = -3/9
Simplifying, we get x = -1/3.
3. Next, we set (three x plus five) equal to the negative value of twelve x plus 8:
-(three x + 5) = 12 x + 8
4. Solve this equation for x:
-3x - 5 = 12x + 8
Move the variables to one side and the constants to the other side:
12x + 3x = -5 - 8
15x = -13
x = -13/15
Therefore, the two values of x that satisfy the given equation are x = -1/3 and x = -13/15.