|3x-2|+4<7
To solve the inequality |3x-2| + 4 < 7, we need to isolate x.
Let's go step by step:
1. Subtract 4 from both sides of the inequality:
|3x-2| < 3
2. We now have two cases to consider:
Case 1: (3x-2) is positive:
In this case, we can drop the absolute value signs, so we have:
3x - 2 < 3
Case 2: (3x-2) is negative:
In this case, we need to change the sign when removing the absolute value signs, so we have:
-(3x - 2) < 3
3. Solving each case separately:
Case 1:
Solve the inequality 3x - 2 < 3:
Add 2 to both sides:
3x < 5
Divide both sides by 3:
x < 5/3
Case 2:
Solve the inequality -(3x - 2) < 3:
Distribute the negative sign:
-3x + 2 < 3
Subtract 2 from both sides:
-3x < 1
Divide both sides by -3 (remember to flip the inequality sign when dividing by a negative number):
x > -1/3
4. Combining the solutions for each case:
The solution when (3x-2) is positive is x < 5/3.
The solution when (3x-2) is negative is x > -1/3.
So, the combined solution is:
x < 5/3 or x > -1/3
Therefore, the solution to the inequality |3x-2| + 4 < 7 is x < 5/3 or x > -1/3.