Question: -3 < t - 4 < 7

Solution

To solve the inequality \[ -3 < 1 - 4x < 7 \] we’ll break it into two separate inequalities and solve each one. First, solve the left part: \[ -3 < 1 - 4x \] Subtract 1 from both sides: \[ -3 - 1 < -4x \] \[ -4 < -4x \] Divide both sides by -4, and reverse the inequality sign: \[ 1 > x \] Now, solve the right part: \[ 1 - 4x < 7 \] Subtract 1 from both sides: \[ -4x < 6 \] Divide both sides by -4, and reverse the inequality sign: \[ x > -\frac{3}{2} \] Combine the two inequalities: \[ -\frac{3}{2} < x < 1 \] So, the solution is \[ x \in \left( -\frac{3}{2}, 1 \right) \]