Solve x-(7x-3)<7-4x-5

$$x - ( 7 x - 3 ) < 7 - 4 x - 5$$

Solve for x

$$x>\frac{1}{2}$$

Solution Steps

To find the opposite of 7x-3, find the opposite of each term.

$$x-7x-\left(-3\right)<7-4x-5$$

The opposite of -3 is 3.

$$x-7x+3<7-4x-5$$

Combine x and -7x to get -6x.

$$-6x+3<7-4x-5$$

Subtract 5 from 7 to get 2.

$$-6x+3<2-4x$$

Add 4x to both sides.

$$-6x+3+4x<2$$

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

$$-2x+3<2$$

Subtract 3 from both sides.

$$-2x<2-3$$

Subtract 3 from 2 to get -1.

$$-2x<-1$$

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

$$x>\frac{-1}{-2}$$

Fraction \frac{-1}{-2} can be simplified to \frac{1}{2} by removing the negative sign from both the numerator and the denominator.

$$x>\frac{1}{2}$$