Solve 3(2y-7)geq4(3y+4)

$$3 ( 2 y - 7 ) \geq 4 ( 3 y + 4 )$$

Solve for y

$$y\leq -\frac{37}{6}$$

Solution Steps

Use the distributive property to multiply 3 by 2y-7.

$$6y-21\geq 4\left(3y+4\right)$$

Use the distributive property to multiply 4 by 3y+4.

$$6y-21\geq 12y+16$$

Subtract 12y from both sides.

$$6y-21-12y\geq 16$$

Combine 6y and -12y to get -6y.

$$-6y-21\geq 16$$

Add 21 to both sides.

$$-6y\geq 16+21$$

Add 16 and 21 to get 37.

$$-6y\geq 37$$

Divide both sides by -6. Since -6 is negative, the inequality direction is changed.

$$y\leq -\frac{37}{6}$$