4x+14≥-2-0,8x

To solve the inequality \( 4x + 14 \geq -2 - 0.8x \), follow these steps: 1. **Combine like terms**: First, we want to get all the terms involving \( x \) on one side and the constant terms on the other side. \[ 4x + 0.8x + 14 \geq -2 \] This simplifies to: \[ (4 + 0.8)x + 14 \geq -2 \] or \[ 4.8x + 14 \geq -2 \] 2. **Isolate the variable term**: Subtract 14 from both sides: \[ 4.8x \geq -2 - 14 \] Simplifying the right side gives: \[ 4.8x \geq -16 \] 3. **Solve for \( x \)**: Divide both sides by 4.8: \[ x \geq \frac{-16}{4.8} \] Simplifying the fraction: \[ x \geq -\frac{16}{4.8} = -\frac{16 \div 4}{4.8 \div 4} = -\frac{4}{1.2} = -\frac{40}{12} = -\frac{10}{3} \approx -3.33 \] Thus, the solution to the inequality is: \[ x \geq -\frac{10}{3} \] You can write this in interval notation as: \[ [-\frac{10}{3}, \infty) \]