Sx. solve the following inequalities. a) \( 5 x+8>4 x+3 \) b) \( 3.5 x-24 \geq 1.5 x+1 \) c) \( 14 x-3 \leq 6 x+21 \) (nequalitios -CW 2 d) \( 3(x-4) \geq x+4 \)

**a) Solve \( 5x+8>4x+3 \):** 1. Subtract \( 4x \) from both sides: \[ 5x - 4x + 8 > 3 \quad \Rightarrow \quad x+8>3. \] 2. Subtract \( 8 \) from both sides: \[ x > 3-8 \quad \Rightarrow \quad x > -5. \] **b) Solve \( 3.5x-24 \geq 1.5x+1 \):** 1. Subtract \( 1.5x \) from both sides: \[ 3.5x - 1.5x - 24 \geq 1 \quad \Rightarrow \quad 2x - 24 \geq 1. \] 2. Add \( 24 \) to both sides: \[ 2x \geq 1+24 \quad \Rightarrow \quad 2x \geq 25. \] 3. Divide both sides by \( 2 \): \[ x \geq \frac{25}{2} \quad \text{or} \quad x \geq 12.5. \] **c) Solve \( 14x-3 \leq 6x+21 \):** 1. Subtract \( 6x \) from both sides: \[ 14x - 6x -3 \leq 21 \quad \Rightarrow \quad 8x - 3 \leq 21. \] 2. Add \( 3 \) to both sides: \[ 8x \leq 21+3 \quad \Rightarrow \quad 8x \leq 24. \] 3. Divide both sides by \( 8 \): \[ x \leq \frac{24}{8} \quad \Rightarrow \quad x \leq 3. \] **d) Solve \( 3(x-4) \geq x+4 \):** 1. Expand the left side: \[ 3x - 12 \geq x + 4. \] 2. Subtract \( x \) from both sides: \[ 3x - x - 12 \geq 4 \quad \Rightarrow \quad 2x - 12 \geq 4. \] 3. Add \( 12 \) to both sides: \[ 2x \geq 4+12 \quad \Rightarrow \quad 2x \geq 16. \] 4. Divide both sides by \( 2 \): \[ x \geq \frac{16}{2} \quad \Rightarrow \quad x \geq 8. \]