\( 6 y+2<-4 \) and \( -4(2 y+3)<-68 \) Solution no solution Interval Notation

To solve the system of inequalities: 1. **First Inequality:** \[ 6y + 2 < -4 \] - Subtract 2 from both sides: \[ 6y < -6 \] - Divide both sides by 6: \[ y < -1 \] 2. **Second Inequality:** \[ -4(2y + 3) < -68 \] - Divide both sides by -4 (remember to reverse the inequality sign when dividing by a negative number): \[ 2y + 3 > 17 \] - Subtract 3 from both sides: \[ 2y > 14 \] - Divide both sides by 2: \[ y > 7 \] **Combining the Results:** - The first inequality requires \( y < -1 \). - The second inequality requires \( y > 7 \). There is **no real number** that satisfies both conditions simultaneously. Therefore, the system has **no solution**. **Interval Notation:** Since there is no solution, the interval is represented by the empty set symbol: \[ \varnothing \] Answer: There is no solution. In interval notation, the solution set is  ∅.