Solve 7-9y/2+14leq6y-10/3-19y

$$\frac { 7 - 9 y } { 2 } + 14 \leq \frac { 6 y - 10 } { 3 } - 19 y$$

Solve for y

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

Solution Steps

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

$$3\left(7-9y\right)+84\leq 2\left(6y-10\right)-114y$$

Use the distributive property to multiply 3 by 7-9y.

$$21-27y+84\leq 2\left(6y-10\right)-114y$$

Add 21 and 84 to get 105.

$$105-27y\leq 2\left(6y-10\right)-114y$$

Use the distributive property to multiply 2 by 6y-10.

$$105-27y\leq 12y-20-114y$$

Combine 12y and -114y to get -102y.

$$105-27y\leq -102y-20$$

Add 102y to both sides.

$$105-27y+102y\leq -20$$

Combine -27y and 102y to get 75y.

$$105+75y\leq -20$$

Subtract 105 from both sides.

$$75y\leq -20-105$$

Subtract 105 from -20 to get -125.

$$75y\leq -125$$

Divide both sides by 75. Since 75 is positive, the inequality direction remains the same.

$$y\leq \frac{-125}{75}$$

Reduce the fraction \frac{-125}{75} to lowest terms by extracting and canceling out 25.

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