Solve 5x-3/4-1+2x/2<2left(1-3xright)

$$\frac{ 5x-3 }{ 4 } - \frac{ 1+2x }{ 2 } < 2 \left( 1-3x \right)$$

Solve for x

$$x<\frac{13}{25}$$

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.

$$5x-3-2\left(1+2x\right)<8\left(1-3x\right)$$

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

$$5x-3-2-4x<8\left(1-3x\right)$$

Subtract 2 from -3 to get -5.

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

Combine 5x 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 25x.

$$25x-5<8$$

Add 5 to both sides.

$$25x<8+5$$

Add 8 and 5 to get 13.

$$25x<13$$

Divide both sides by 25. Since 25 is positive, the inequality direction remains the same.

$$x<\frac{13}{25}$$