Solve -3x-7-2(x-5)leq2(x-5.5)

$$- 3 x - 7 - 2 ( x - 5 ) \leq 2 ( x - 5.5 )$$

Solve for x

$$x\geq 2$$

Solution Steps

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

$$-3x-7-2x+10\leq 2\left(x-5.5\right)$$

Combine -3x and -2x to get -5x.

$$-5x-7+10\leq 2\left(x-5.5\right)$$

Add -7 and 10 to get 3.

$$-5x+3\leq 2\left(x-5.5\right)$$

Use the distributive property to multiply 2 by x-5.5.

$$-5x+3\leq 2x-11$$

Subtract 2x from both sides.

$$-5x+3-2x\leq -11$$

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

$$-7x+3\leq -11$$

Subtract 3 from both sides.

$$-7x\leq -11-3$$

Subtract 3 from -11 to get -14.

$$-7x\leq -14$$

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

$$x\geq \frac{-14}{-7}$$

Divide -14 by -7 to get 2.

$$x\geq 2$$