Please help me solve this inequality problem.
|1-(4)/(3)x|<3
if this your problem
| 1 - 4x/3 | < 3
remove absolute value sign
1 - 4x/3 < 3 and
-1 + 4x/3 < 3
1 - 4x/3 < 3
-4x/3 < 2
-4x < 6
x > -6/4
x > -3/2
-1 + 4x/3 < 3
4x/3 < 4
4x < 12
x < 3
so solution is
-3/2 < x < 3
To solve the inequality |1-(4/3)x| < 3, we need to break it down into two separate inequalities without the absolute value sign.
First, consider the case when 1-(4/3)x is positive:
1 - (4/3)x < 3
To start solving this inequality, we can subtract 1 from both sides:
-(4/3)x < 2
Next, multiply both sides by -3/4. Pay attention to the sign flip:
(4/3)x > -3/2
Now, consider the case when 1-(4/3)x is negative:
-(1 - (4/3)x) < 3
To simplify this inequality, let's distribute the negative sign:
-1 + (4/3)x < 3
Adding 1 to both sides:
(4/3)x < 4
We can divide both sides by 4/3. Since dividing by a positive number, the inequality sign will not be flipped:
x < 3
Now we have the solutions for the two cases: x > -3/2 and x < 3.
Combining the solutions:
x > -3/2 and x < 3
So, the solution to the inequality |1-(4/3)x| < 3 is -3/2 < x < 3.