Solve x+5(3-2x)+2geq2(x+3)+3x+1

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

Solve for x

$$x\leq \frac{5}{7}$$

Solution Steps

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

$$x+15-10x+2\geq 2\left(x+3\right)+3x+1$$

Combine x and -10x to get -9x.

$$-9x+15+2\geq 2\left(x+3\right)+3x+1$$

Add 15 and 2 to get 17.

$$-9x+17\geq 2\left(x+3\right)+3x+1$$

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

$$-9x+17\geq 2x+6+3x+1$$

Combine 2x and 3x to get 5x.

$$-9x+17\geq 5x+6+1$$

Add 6 and 1 to get 7.

$$-9x+17\geq 5x+7$$

Subtract 5x from both sides.

$$-9x+17-5x\geq 7$$

Combine -9x and -5x to get -14x.

$$-14x+17\geq 7$$

Subtract 17 from both sides.

$$-14x\geq 7-17$$

Subtract 17 from 7 to get -10.

$$-14x\geq -10$$

Divide both sides by -14. Since -14 is negative, the inequality direction is changed.

$$x\leq \frac{-10}{-14}$$

Reduce the fraction \frac{-10}{-14} to lowest terms by extracting and canceling out -2.

$$x\leq \frac{5}{7}$$