Solve -4(8-y)geq7(y-2)-y

$$- 4 ( 8 - y ) \geq 7 ( y - 2 ) - y$$

Solve for y

$$y\leq -9$$

Solution Steps

Use the distributive property to multiply -4 by 8-y.

$$-32+4y\geq 7\left(y-2\right)-y$$

Use the distributive property to multiply 7 by y-2.

$$-32+4y\geq 7y-14-y$$

Combine 7y and -y to get 6y.

$$-32+4y\geq 6y-14$$

Subtract 6y from both sides.

$$-32+4y-6y\geq -14$$

Combine 4y and -6y to get -2y.

$$-32-2y\geq -14$$

Add 32 to both sides.

$$-2y\geq -14+32$$

Add -14 and 32 to get 18.

$$-2y\geq 18$$

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

$$y\leq \frac{18}{-2}$$

Divide 18 by -2 to get -9.

$$y\leq -9$$