Solve 5(2g-3)-6ggeq-2(g-6)+3

$$5 ( 2 g - 3 ) - 6 g \geq - 2 ( g - 6 ) + 3$$

Solve for g

$$g\geq 5$$

Solution Steps

Use the distributive property to multiply 5 by 2g-3.

$$10g-15-6g\geq -2\left(g-6\right)+3$$

Combine 10g and -6g to get 4g.

$$4g-15\geq -2\left(g-6\right)+3$$

Use the distributive property to multiply -2 by g-6.

$$4g-15\geq -2g+12+3$$

Add 12 and 3 to get 15.

$$4g-15\geq -2g+15$$

Add 2g to both sides.

$$4g-15+2g\geq 15$$

Combine 4g and 2g to get 6g.

$$6g-15\geq 15$$

Add 15 to both sides.

$$6g\geq 15+15$$

Add 15 and 15 to get 30.

$$6g\geq 30$$

Divide both sides by 6. Since 6 is positive, the inequality direction remains the same.

$$g\geq \frac{30}{6}$$

Divide 30 by 6 to get 5.

$$g\geq 5$$