Solve 3*(x+3)+2geq5*(2x+9)-6

$$3 \cdot ( x + 3 ) + 2 \geq 5 \cdot ( 2 x + 9 ) - 6$$

Solve for x

$$x\leq -4$$

Solution Steps

Use the distributive property to multiply 3 by x+3.

$$3x+9+2\geq 5\left(2x+9\right)-6$$

Add 9 and 2 to get 11.

$$3x+11\geq 5\left(2x+9\right)-6$$

Use the distributive property to multiply 5 by 2x+9.

$$3x+11\geq 10x+45-6$$

Subtract 6 from 45 to get 39.

$$3x+11\geq 10x+39$$

Subtract 10x from both sides.

$$3x+11-10x\geq 39$$

Combine 3x and -10x to get -7x.

$$-7x+11\geq 39$$

Subtract 11 from both sides.

$$-7x\geq 39-11$$

Subtract 11 from 39 to get 28.

$$-7x\geq 28$$

Divide both sides by -7. Since -7 is negative, the inequality direction is changed.

$$x\leq \frac{28}{-7}$$

Divide 28 by -7 to get -4.

$$x\leq -4$$