Solve 2x-(x+3)-7leq4(x+1)-2(5-x)+16

$$2 x - ( x + 3 ) - 7 \leq 4 ( x + 1 ) - 2 ( 5 - x ) + 16$$

Solve for x

$$x\geq -4$$

Solution Steps

To find the opposite of x+3, find the opposite of each term.

$$2x-x-3-7\leq 4\left(x+1\right)-2\left(5-x\right)+16$$

Combine 2x and -x to get x.

$$x-3-7\leq 4\left(x+1\right)-2\left(5-x\right)+16$$

Subtract 7 from -3 to get -10.

$$x-10\leq 4\left(x+1\right)-2\left(5-x\right)+16$$

Use the distributive property to multiply 4 by x+1.

$$x-10\leq 4x+4-2\left(5-x\right)+16$$

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

$$x-10\leq 4x+4-10+2x+16$$

Subtract 10 from 4 to get -6.

$$x-10\leq 4x-6+2x+16$$

Combine 4x and 2x to get 6x.

$$x-10\leq 6x-6+16$$

Add -6 and 16 to get 10.

$$x-10\leq 6x+10$$

Subtract 6x from both sides.

$$x-10-6x\leq 10$$

Combine x and -6x to get -5x.

$$-5x-10\leq 10$$

Add 10 to both sides.

$$-5x\leq 10+10$$

Add 10 and 10 to get 20.

$$-5x\leq 20$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$x\geq \frac{20}{-5}$$

Divide 20 by -5 to get -4.

$$x\geq -4$$