Solve -3(2x+3)+2geq9/3(3x+1)

$$- 3 ( 2 x + 3 ) + 2 \geq \frac { 9 } { 3 } ( 3 x + 1 )$$

Solve for x

$$x\leq -\frac{2}{3}$$

Solution Steps

Use the distributive property to multiply -3 by 2x+3.

$$-6x-9+2\geq \frac{9}{3}\left(3x+1\right)$$

Add -9 and 2 to get -7.

$$-6x-7\geq \frac{9}{3}\left(3x+1\right)$$

Divide 9 by 3 to get 3.

$$-6x-7\geq 3\left(3x+1\right)$$

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

$$-6x-7\geq 9x+3$$

Subtract 9x from both sides.

$$-6x-7-9x\geq 3$$

Combine -6x and -9x to get -15x.

$$-15x-7\geq 3$$

Add 7 to both sides.

$$-15x\geq 3+7$$

Add 3 and 7 to get 10.

$$-15x\geq 10$$

Divide both sides by -15. Since -15 is negative, the inequality direction is changed.

$$x\leq \frac{10}{-15}$$

Reduce the fraction \frac{10}{-15} to lowest terms by extracting and canceling out 5.

$$x\leq -\frac{2}{3}$$