Solve 3x-5(2x+4)leq-5(x-1)-2(x+1)

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

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

Use the distributive property to multiply -5 by 2x+4.

$$3x-10x-20\leq -5\left(x-1\right)-2\left(x+1\right)$$

Combine 3x and -10x to get -7x.

$$-7x-20\leq -5\left(x-1\right)-2\left(x+1\right)$$

Use the distributive property to multiply -5 by x-1.

$$-7x-20\leq -5x+5-2\left(x+1\right)$$

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

$$-7x-20\leq -5x+5-2x-2$$

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

$$-7x-20\leq -7x+5-2$$

Subtract 2 from 5 to get 3.

$$-7x-20\leq -7x+3$$

Add 7x to both sides.

$$-7x-20+7x\leq 3$$

Combine -7x and 7x to get 0.

$$-20\leq 3$$

This is true for any x.

$$x\in \mathrm{R}$$