Solve -(1-2x)-5xleq-(1+x)-4

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

Solve for x

$$x\geq 2$$

Solution Steps

To find the opposite of 1-2x, find the opposite of each term.

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

The opposite of -2x is 2x.

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

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

$$-1-3x\leq -\left(1+x\right)-4$$

To find the opposite of 1+x, find the opposite of each term.

$$-1-3x\leq -1-x-4$$

Subtract 4 from -1 to get -5.

$$-1-3x\leq -5-x$$

Add x to both sides.

$$-1-3x+x\leq -5$$

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

$$-1-2x\leq -5$$

Add 1 to both sides.

$$-2x\leq -5+1$$

Add -5 and 1 to get -4.

$$-2x\leq -4$$

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

$$x\geq \frac{-4}{-2}$$

Divide -4 by -2 to get 2.

$$x\geq 2$$