1<3x+5<12
1 < 3x+5 < 12
-4 < 3x < 7
-4/3 < x < 7/3
To solve the inequality 1 < 3x + 5 < 12, we need to isolate the variable, x. Here's how you can do it step by step:
1. Subtract 5 from all three parts of the inequality:
1 - 5 < 3x + 5 - 5 < 12 - 5
-4 < 3x < 7
2. Divide all parts of the inequality by 3 (since we want to isolate x):
-4/3 < 3x/3 < 7/3
-4/3 < x < 7/3
So, the solution to the inequality is -4/3 < x < 7/3. This means that any value of x within this range will satisfy the original inequality.