Solve 2(2.4z+3.5)geq-12.2

$$2 ( 2.4 z + 3.5 ) \geq - 12.2$$

Solve for z

$$z\geq -4$$

Solution Steps

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

$$2.4z+3.5\geq \frac{-12.2}{2}$$

Expand \frac{-12.2}{2} by multiplying both numerator and the denominator by 10.

$$2.4z+3.5\geq \frac{-122}{20}$$

Reduce the fraction \frac{-122}{20} to lowest terms by extracting and canceling out 2.

$$2.4z+3.5\geq -\frac{61}{10}$$

Subtract 3.5 from both sides.

$$2.4z\geq -\frac{61}{10}-3.5$$

Convert decimal number 3.5 to fraction \frac{35}{10}. Reduce the fraction \frac{35}{10} to lowest terms by extracting and canceling out 5.

$$2.4z\geq -\frac{61}{10}-\frac{7}{2}$$

Least common multiple of 10 and 2 is 10. Convert -\frac{61}{10} and \frac{7}{2} to fractions with denominator 10.

$$2.4z\geq -\frac{61}{10}-\frac{35}{10}$$

Since -\frac{61}{10} and \frac{35}{10} have the same denominator, subtract them by subtracting their numerators.

$$2.4z\geq \frac{-61-35}{10}$$

Subtract 35 from -61 to get -96.

$$2.4z\geq \frac{-96}{10}$$

Reduce the fraction \frac{-96}{10} to lowest terms by extracting and canceling out 2.

$$2.4z\geq -\frac{48}{5}$$

Divide both sides by 2.4. Since 2.4 is positive, the inequality direction remains the same.

$$z\geq \frac{-\frac{48}{5}}{2.4}$$

Express \frac{-\frac{48}{5}}{2.4} as a single fraction.

$$z\geq \frac{-48}{5\times 2.4}$$

Multiply 5 and 2.4 to get 12.

$$z\geq \frac{-48}{12}$$

Divide -48 by 12 to get -4.

$$z\geq -4$$