Solve the following continued inequalities. Write your answers with interval notation.
−210<70x−70<210
−210<70x−70<210
divide by 70
−3 < x−1 < 3
add 1
−2 < x < 4
- 210 < 70 x - 70 < 210
Divide all sides by 70
- 3 < x - 1 < 3
Add1 to all sides
- 2 < x < 4
( - 2 , 4 )
To solve the given inequality, we need to isolate the variable x. We'll do this step by step:
1. Subtract 70 from all three parts of the inequality:
-210 < 70x - 70 < 210
-210 + 70 < 70x - 70 + 70 < 210 + 70
-140 < 70x < 280
2. Divide all three parts of the inequality by 70 (the coefficient of x):
-140/70 < 70x/70 < 280/70
-2 < x < 4
3. Now we have the solution for x, but we need to write it in interval notation. In interval notation, we use parentheses for open intervals and square brackets for closed intervals.
So, the solution in interval notation is (-2, 4).