Final answer:
To solve the absolute value equation 2|5x|+5=17, isolate the absolute value, resulting in |5x|=6. This leads to two equations: 5x=6 and 5x=-6, giving two valid solutions, x=1.2 and x=-1.2.
Step-by-step explanation:
To solve the equation 2|5x|+5=17, we first isolate the absolute value on one side of the equation by subtracting 5 from both sides:
2|5x| = 12
Now, divide both sides by 2 to get the absolute value by itself:
|5x| = 6
This leads to two possible equations, since the absolute value of a number could be the positive or negative version of that number:
- 5x = 6
- 5x = -6
Solving both equations for x, we get:
- x = 6 / 5
- x = -6 / 5
These solutions give us x = 1.2 or x = -1.2. Both solutions are valid as they satisfy the original absolute value equation.