this question is a multiple choice question, however i don't know how to start or finish it.
The solution set of |3x+2|<1 contains...
i need help trying to figure out how to solve for x. other then that i believe i could answer the question.
x>-1/3
To solve the inequality |3x+2|<1, we need to consider two cases:
Case 1: (3x+2) is positive or zero:
In this case, the inequality becomes 3x+2<1. Let's solve it step-by-step:
1. Subtract 2 from both sides:
3x + 2 - 2 < 1 - 2
3x < -1
2. Divide both sides by 3:
(3x)/3 < (-1)/3
x < -1/3
So, for the first case, the solution is x < -1/3.
Case 2: (3x+2) is negative:
In this case, the inequality becomes -(3x+2) < 1. Note that when we multiply by -1 on both sides of an inequality, the direction of the inequality sign switches. Let's solve it step-by-step:
1. Distribute the negative sign:
-3x - 2 < 1
2. Add 2 to both sides:
-3x < 1 + 2
-3x < 3
3. Divide both sides by -3, remembering that when we divide by a negative number, the direction of the inequality sign switches:
(-3x)/(-3) > 3/(-3)
x > -1
So, for the second case, the solution is x > -1.
Combining the solutions from both cases, we have the interval notation: -1 < x < -1/3.
To solve the inequality |3x+2|<1, you need to consider two cases: when the expression inside the absolute value is positive and when it is negative.
Case 1: 3x+2 > 0
In this case, the absolute value |3x+2| is equal to (3x+2). So the inequality becomes 3x+2 < 1. Now, solve for x:
3x + 2 < 1
3x < 1 - 2
3x < -1
x < -1/3
Case 2: 3x+2 < 0
In this case, the absolute value |3x+2| is equal to -(3x+2). So the inequality becomes -(3x+2) < 1. Now, solve for x:
-(3x+2) < 1
-3x - 2 < 1
-3x < 1 + 2
-3x < 3
x > -1
Now, by combining the solutions of both cases, we can determine the solution set of the inequality |3x+2|<1:
x < -1/3 or x > -1
So, the solution set of the inequality |3x+2|<1 contains all values of x that are less than -1/3 or greater than -1.