Solve −3 < 2x + 1 ≤ 5
Compound inequality, worked out line by line the way a teacher would write it.
Answer
| Solution | −2 < x ≤ 2 |
| Interval notation | (−2, 2] |
Step-by-step solution
4 steps-
1 Given-3 < 2 x + 1 \le 5
Solve for x.
-
2 Subtract 1 from all three parts
A compound inequality is two inequalities at once. Doing the same operation to all three parts keeps both of them true, which isolates the variable in the middle.
-4 < 2 x \le 4 -
3 Divide all three parts by 2-2 < x \le 2
-
4 Solution-2 < x \le 2\qquad \left( -2, 2 \right]
Check with test values
| x | Left | Middle | Right | Holds? |
|---|---|---|---|---|
| −1 | −3 | −1 | 5 | ✓ true |
| −3 | −3 | −5 | 5 | ✗ false |
Open this problem in the solver
Change a number or try your own problem: the solver works it out the same way, with a graph and hint mode.