Solve -(x+1)+4left(2x-3right)<2x

$$-(x+1)+4 \left( 2x-3 \right) < 2x$$

Solve for x

$$x<\frac{13}{5}$$

Solution Steps

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

$$-x-1+4\left(2x-3\right)<2x$$

Use the distributive property to multiply 4 by 2x-3.

$$-x-1+8x-12<2x$$

Combine -x and 8x to get 7x.

$$7x-1-12<2x$$

Subtract 12 from -1 to get -13.

$$7x-13<2x$$

Subtract 2x from both sides.

$$7x-13-2x<0$$

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

$$5x-13<0$$

Add 13 to both sides. Anything plus zero gives itself.

$$5x<13$$

Divide both sides by 5. Since 5 is positive, the inequality direction remains the same.

$$x<\frac{13}{5}$$