Solve (3-2x)+2geq2(x+3)+3x+1

$$( 3 - 2 x ) + 2 \geq 2 ( x + 3 ) + 3 x + 1$$

Solve for x

$$x\leq -\frac{2}{7}$$

Solution Steps

Add 3 and 2 to get 5.

$$5-2x\geq 2\left(x+3\right)+3x+1$$

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

$$5-2x\geq 2x+6+3x+1$$

Combine 2x and 3x to get 5x.

$$5-2x\geq 5x+6+1$$

Add 6 and 1 to get 7.

$$5-2x\geq 5x+7$$

Subtract 5x from both sides.

$$5-2x-5x\geq 7$$

Combine -2x and -5x to get -7x.

$$5-7x\geq 7$$

Subtract 5 from both sides.

$$-7x\geq 7-5$$

Subtract 5 from 7 to get 2.

$$-7x\geq 2$$

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

$$x\leq -\frac{2}{7}$$