How to solve 2x-1/3 >= (3x-2))

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 2x-1/3 >= (3x-2)) | Equatix

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Question

$$2x-1/3 \geq (3x-2))$$

Solve for x

$x\leq \frac{5}{3}$

Solution Steps

Subtract $3x$ from both sides.

$$2x-\frac{1}{3}-3x\geq -2$$

Combine $2x$ and $-3x$ to get $-x$.

$$-x-\frac{1}{3}\geq -2$$

Add $\frac{1}{3}$ to both sides.

$$-x\geq -2+\frac{1}{3}$$

Convert $-2$ to fraction $-\frac{6}{3}$.

$$-x\geq -\frac{6}{3}+\frac{1}{3}$$

Since $-\frac{6}{3}$ and $\frac{1}{3}$ have the same denominator, add them by adding their numerators.

$$-x\geq \frac{-6+1}{3}$$

Add $-6$ and $1$ to get $-5$.

$$-x\geq -\frac{5}{3}$$

Divide both sides by $-1$. Since $-1$ is negative, the inequality direction is changed.

$$x\leq \frac{-\frac{5}{3}}{-1}$$

Express $\frac{-\frac{5}{3}}{-1}$ as a single fraction.

$$x\leq \frac{-5}{3\left(-1\right)}$$

Multiply $3$ and $-1$ to get $-3$.

$$x\leq \frac{-5}{-3}$$

Fraction $\frac{-5}{-3}$ can be simplified to $\frac{5}{3}$ by removing the negative sign from both the numerator and the denominator.

$$x\leq \frac{5}{3}$$

Show Solution