Solve 2y-1/3-3y-1/2geq5/12

$$\frac { 2 y - 1 } { 3 } - \frac { 3 y - 1 } { 2 } \geq \frac { 5 } { 12 }$$

Solve for y

$$y\leq -\frac{3}{10}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 3,2,12. Since 12 is positive, the inequality direction remains the same.

$$4\left(2y-1\right)-6\left(3y-1\right)\geq 5$$

Use the distributive property to multiply 4 by 2y-1.

$$8y-4-6\left(3y-1\right)\geq 5$$

Use the distributive property to multiply -6 by 3y-1.

$$8y-4-18y+6\geq 5$$

Combine 8y and -18y to get -10y.

$$-10y-4+6\geq 5$$

Add -4 and 6 to get 2.

$$-10y+2\geq 5$$

Subtract 2 from both sides.

$$-10y\geq 5-2$$

Subtract 2 from 5 to get 3.

$$-10y\geq 3$$

Divide both sides by -10. Since -10 is negative, the inequality direction is changed.

$$y\leq -\frac{3}{10}$$