Solve 2(3x-2)-5x+7leq2(x+1)

$$2 ( 3 x - 2 ) - 5 x + 7 \leq 2 ( x + 1 )$$

Solve for x

$$x\geq 1$$

Solution Steps

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

$$6x-4-5x+7\leq 2\left(x+1\right)$$

Combine 6x and -5x to get x.

$$x-4+7\leq 2\left(x+1\right)$$

Add -4 and 7 to get 3.

$$x+3\leq 2\left(x+1\right)$$

Use the distributive property to multiply 2 by x+1.

$$x+3\leq 2x+2$$

Subtract 2x from both sides.

$$x+3-2x\leq 2$$

Combine x and -2x to get -x.

$$-x+3\leq 2$$

Subtract 3 from both sides.

$$-x\leq 2-3$$

Subtract 3 from 2 to get -1.

$$-x\leq -1$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x\geq \frac{-1}{-1}$$

Divide -1 by -1 to get 1.

$$x\geq 1$$