Solve 2/3(2y-5)leqy+8/6+7

$$\frac { 2 } { 3 } ( 2 y - 5 ) \leq \frac { y + 8 } { 6 } + 7$$

Solve for y

$$y\leq 10$$

Solution Steps

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

$$4\left(2y-5\right)\leq y+8+42$$

Use the distributive property to multiply 4 by 2y-5.

$$8y-20\leq y+8+42$$

Add 8 and 42 to get 50.

$$8y-20\leq y+50$$

Subtract y from both sides.

$$8y-20-y\leq 50$$

Combine 8y and -y to get 7y.

$$7y-20\leq 50$$

Add 20 to both sides.

$$7y\leq 50+20$$

Add 50 and 20 to get 70.

$$7y\leq 70$$

Divide both sides by 7. Since 7 is positive, the inequality direction remains the same.

$$y\leq \frac{70}{7}$$

Divide 70 by 7 to get 10.

$$y\leq 10$$