Solve y-1/2-2leq3y-2/5

$$\frac { y - 1 } { 2 } - 2 \leq \frac { 3 y - 2 } { 5 }$$

Solve for y

$$y\geq -21$$

Solution Steps

Multiply both sides of the equation by 10, the least common multiple of 2,5. Since 10 is positive, the inequality direction remains the same.

$$5\left(y-1\right)-20\leq 2\left(3y-2\right)$$

Use the distributive property to multiply 5 by y-1.

$$5y-5-20\leq 2\left(3y-2\right)$$

Subtract 20 from -5 to get -25.

$$5y-25\leq 2\left(3y-2\right)$$

Use the distributive property to multiply 2 by 3y-2.

$$5y-25\leq 6y-4$$

Subtract 6y from both sides.

$$5y-25-6y\leq -4$$

Combine 5y and -6y to get -y.

$$-y-25\leq -4$$

Add 25 to both sides.

$$-y\leq -4+25$$

Add -4 and 25 to get 21.

$$-y\leq 21$$

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

$$y\geq -21$$