(8) Show that the solution set to the inequality \( 4(2 y+3)-5 y<18-y \) is \( y<1.5 \) (bubstitute \( \mathbf{i} y=1 \), ii \( y=1.5 \) and iii \( y=2 \) into \( 4(2 y+3)-5 y<18-y \) to show that the solution set is correct.

To solve the inequality \( 4(2y+3) - 5y < 18 - y \), we first simplify the left side: 1. Distributing the 4: \[ 8y + 12 - 5y < 18 - y \] 2. Combining like terms: \[ 3y + 12 < 18 - y \] 3. Adding \( y \) to both sides: \[ 3y + y + 12 < 18 \] \[ 4y + 12 < 18 \] 4. Subtracting 12 from both sides: \[ 4y < 6 \] 5. Dividing by 4: \[ y < 1.5 \] Now, let's verify this by substituting the suggested values. 1. For \( y = 1 \): \[ 4(2(1) + 3) - 5(1) < 18 - 1 \] \[ 4(5) - 5 < 17 \] \[ 20 - 5 < 17 \] \[ 15 < 17 \, \text{(True!)} \] 2. For \( y = 1.5 \): \[ 4(2(1.5) + 3) - 5(1.5) < 18 - 1.5 \] \[ 4(6) - 7.5 < 16.5 \] \[ 24 - 7.5 < 16.5 \] \[ 16.5 < 16.5 \, \text{(False!)} \] 3. For \( y = 2 \): \[ 4(2(2) + 3) - 5(2) < 18 - 2 \] \[ 4(7) - 10 < 16 \] \[ 28 - 10 < 16 \] \[ 18 < 16 \, \text{(False!)} \] The results show that \( y < 1.5 \) is the correct solution set since both \( y = 1 \) fits, whereas \( y = 1.5 \) and \( y = 2 \) do not satisfy the inequality.