Solve 1-2m/3geq3m-1/2

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

Solve for m

$$m\leq \frac{5}{13}$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2. Since 6 is positive, the inequality direction remains the same.

$$2\left(1-2m\right)\geq 3\left(3m-1\right)$$

Use the distributive property to multiply 2 by 1-2m.

$$2-4m\geq 3\left(3m-1\right)$$

Use the distributive property to multiply 3 by 3m-1.

$$2-4m\geq 9m-3$$

Subtract 9m from both sides.

$$2-4m-9m\geq -3$$

Combine -4m and -9m to get -13m.

$$2-13m\geq -3$$

Subtract 2 from both sides.

$$-13m\geq -3-2$$

Subtract 2 from -3 to get -5.

$$-13m\geq -5$$

Divide both sides by -13. Since -13 is negative, the inequality direction is changed.

$$m\leq \frac{-5}{-13}$$

Fraction \frac{-5}{-13} can be simplified to \frac{5}{13} by removing the negative sign from both the numerator and the denominator.

$$m\leq \frac{5}{13}$$