Solve y-2/9-4y-1/6geq1-8-y/18

$$\frac{ y-2 }{ 9 } - \frac{ 4y-1 }{ 6 } \geq 1- \frac{ 8-y }{ 18 }$$

Solve for y

$$y\leq -1$$

Solution Steps

Multiply both sides of the equation by 18, the least common multiple of 9,6,18. Since 18 is positive, the inequality direction remains the same.

$$2\left(y-2\right)-3\left(4y-1\right)\geq 18-\left(8-y\right)$$

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

$$2y-4-3\left(4y-1\right)\geq 18-\left(8-y\right)$$

Use the distributive property to multiply -3 by 4y-1.

$$2y-4-12y+3\geq 18-\left(8-y\right)$$

Combine 2y and -12y to get -10y.

$$-10y-4+3\geq 18-\left(8-y\right)$$

Add -4 and 3 to get -1.

$$-10y-1\geq 18-\left(8-y\right)$$

To find the opposite of 8-y, find the opposite of each term.

$$-10y-1\geq 18-8-\left(-y\right)$$

The opposite of -y is y.

$$-10y-1\geq 18-8+y$$

Subtract 8 from 18 to get 10.

$$-10y-1\geq 10+y$$

Subtract y from both sides.

$$-10y-1-y\geq 10$$

Combine -10y and -y to get -11y.

$$-11y-1\geq 10$$

Add 1 to both sides.

$$-11y\geq 10+1$$

Add 10 and 1 to get 11.

$$-11y\geq 11$$

Divide both sides by -11. Since -11 is negative, the inequality direction is changed.

$$y\leq \frac{11}{-11}$$

Divide 11 by -11 to get -1.

$$y\leq -1$$