Solve, express your answer in interval notation absolute value of 3x-10 is > 2
|3x-10) > 2
either
3x-10 > 2
3x > 12
x > 4
or
-(3x-10) > 2
3x-10 < -2
3x < 8
x < 8/3
If you look at the graph you can see why an abs val > n problem usually has two solutions.
http://www.wolframalpha.com/input/?i=+|3x-10|+%3E+2
To solve the inequality |3x - 10| > 2, we can break it down into two separate inequalities:
1. 3x - 10 > 2
2. -(3x - 10) > 2
Let's solve each inequality step by step:
1. 3x - 10 > 2
Add 10 to both sides: 3x > 12
Divide both sides by 3 (since the coefficient of x is 3): x > 4
2. -(3x - 10) > 2
Distribute the negative sign: -3x + 10 > 2
Subtract 10 from both sides: -3x > -8
Divide both sides by -3 (remember to flip the inequality sign since we are dividing by a negative number): x < 8/3
Now, let's express the solution in interval notation. We have two separate inequalities:
1. For x > 4, we can use the notation (4, ∞) to represent the interval from 4 to positive infinity.
2. For x < 8/3, we can use the notation (-∞, 8/3) to represent the interval from negative infinity to 8/3.
Combining these two intervals, we get the solution in interval notation as (-∞, 8/3) ∪ (4, ∞). This means that the values of x that satisfy the inequality |3x - 10| > 2 are all real numbers less than 8/3 and all real numbers greater than 4.