Solve 3(5-2x)+2leq7-2(x+1)

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

Solve for x

$$x\geq 3$$

Solution Steps

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

$$15-6x+2\leq 7-2\left(x+1\right)$$

Add 15 and 2 to get 17.

$$17-6x\leq 7-2\left(x+1\right)$$

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

$$17-6x\leq 7-2x-2$$

Subtract 2 from 7 to get 5.

$$17-6x\leq 5-2x$$

Add 2x to both sides.

$$17-6x+2x\leq 5$$

Combine -6x and 2x to get -4x.

$$17-4x\leq 5$$

Subtract 17 from both sides.

$$-4x\leq 5-17$$

Subtract 17 from 5 to get -12.

$$-4x\leq -12$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

$$x\geq \frac{-12}{-4}$$

Divide -12 by -4 to get 3.

$$x\geq 3$$