4x+14≥-2-0,8x
To solve the inequality \( 4x + 14 \geq -2 - 0.8x \), follow these steps:
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
\[ 4.8x + 14 \geq -2 \]
Isolate the variable term: Subtract 14 from both sides:
\[ 4.8x \geq -2 - 14 \]
Simplifying the right side gives:
\[ 4.8x \geq -16 \]
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:
\[ [-\frac{10}{3}, \infty) \]
