Solve 2+3(y+1)/8leq2-y-3/4

$$2 + \frac { 3 ( y + 1 ) } { 8 } \leq 2 - \frac { y - 3 } { 4 }$$

Solve for y

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

Solution Steps

Multiply both sides of the equation by 8, the least common multiple of 8,4. Since 8 is positive, the inequality direction remains the same.

$$16+3\left(y+1\right)\leq 16-2\left(y-3\right)$$

Use the distributive property to multiply 3 by y+1.

$$16+3y+3\leq 16-2\left(y-3\right)$$

Add 16 and 3 to get 19.

$$19+3y\leq 16-2\left(y-3\right)$$

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

$$19+3y\leq 16-2y+6$$

Add 16 and 6 to get 22.

$$19+3y\leq 22-2y$$

Add 2y to both sides.

$$19+3y+2y\leq 22$$

Combine 3y and 2y to get 5y.

$$19+5y\leq 22$$

Subtract 19 from both sides.

$$5y\leq 22-19$$

Subtract 19 from 22 to get 3.

$$5y\leq 3$$

Divide both sides by 5. Since 5 is positive, the inequality direction remains the same.

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