How to solve -3(6)/(10)x < 9

Q: How to solve -3(6)/(10)x < 9

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve -3(6)/(10)x < 9 | Equatix

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Question

$$-3 \frac{ 6 }{ 10 } x < 9$$

Solve for x

$x>-\frac{5}{2}$

Solution Steps

Multiply both sides of the equation by $10$. Since $10$ is positive, the inequality direction remains the same.

$$10\left(-\frac{3\times 10+6}{10}\right)x<90$$

Multiply $3$ and $10$ to get $30$.

$$10\left(-\frac{30+6}{10}\right)x<90$$

Add $30$ and $6$ to get $36$.

$$10\left(-\frac{36}{10}\right)x<90$$

Reduce the fraction $\frac{36}{10}$ to lowest terms by extracting and canceling out $2$.

$$10\left(-\frac{18}{5}\right)x<90$$

Express $10\left(-\frac{18}{5}\right)$ as a single fraction.

$$\frac{10\left(-18\right)}{5}x<90$$

Multiply $10$ and $-18$ to get $-180$.

$$\frac{-180}{5}x<90$$

Divide $-180$ by $5$ to get $-36$.

$$-36x<90$$

Divide both sides by $-36$. Since $-36$ is negative, the inequality direction is changed.

$$x>\frac{90}{-36}$$

Reduce the fraction $\frac{90}{-36}$ to lowest terms by extracting and canceling out $18$.

$$x>-\frac{5}{2}$$

Show Solution