Solve 3x-3/4-1+2x/2<2(1-3x)

$$\frac { 3 x - 3 } { 4 } - \frac { 1 + 2 x } { 2 } < 2 ( 1 - 3 x )$$

Solve for x

$$x<\frac{13}{23}$$

Solution Steps

Multiply both sides of the equation by 4, the least common multiple of 4,2. Since 4 is positive, the inequality direction remains the same.

$$3x-3-2\left(1+2x\right)<8\left(1-3x\right)$$

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

$$3x-3-2-4x<8\left(1-3x\right)$$

Subtract 2 from -3 to get -5.

$$3x-5-4x<8\left(1-3x\right)$$

Combine 3x and -4x to get -x.

$$-x-5<8\left(1-3x\right)$$

Use the distributive property to multiply 8 by 1-3x.

$$-x-5<8-24x$$

Add 24x to both sides.

$$-x-5+24x<8$$

Combine -x and 24x to get 23x.

$$23x-5<8$$

Add 5 to both sides.

$$23x<8+5$$

Add 8 and 5 to get 13.

$$23x<13$$

Divide both sides by 23. Since 23 is positive, the inequality direction remains the same.

$$x<\frac{13}{23}$$