-7<2x+1<11

Answer 1

To solve the compound inequality \(-7 < 2x + 1 < 11\), we can break it down into two separate inequalities.

1. Solve the left side: \[ -7 < 2x + 1 \] Subtract 1 from both sides: \[ -7 - 1 < 2x \] \[ -8 < 2x \] Now divide by 2: \[ -4 < x \] or \[ x > -4 \]

2. Solve the right side: \[ 2x + 1 < 11 \] Subtract 1 from both sides: \[ 2x < 11 - 1 \] \[ 2x < 10 \] Now divide by 2: \[ x < 5 \]

Now we combine the results from both inequalities: \[ -4 < x < 5 \]

So the solution to the compound inequality is: \[ x \in (-4, 5) \]