Solve 3-4x/1-3x/10>6-x/2

$$\frac { 3 - 4 x } { 1 } - \frac { 3 x } { 10 } > \frac { 6 - x } { 2 }$$

Solve for x

$$x<0$$

Solution Steps

Multiply both sides of the equation by 10, the least common multiple of 10,2. Since 10 is positive, the inequality direction remains the same.

$$10\left(3-4x\right)-3x>5\left(6-x\right)$$

Use the distributive property to multiply 10 by 3-4x.

$$30-40x-3x>5\left(6-x\right)$$

Combine -40x and -3x to get -43x.

$$30-43x>5\left(6-x\right)$$

Use the distributive property to multiply 5 by 6-x.

$$30-43x>30-5x$$

Add 5x to both sides.

$$30-43x+5x>30$$

Combine -43x and 5x to get -38x.

$$30-38x>30$$

Subtract 30 from both sides.

$$-38x>30-30$$

Subtract 30 from 30 to get 0.

$$-38x>0$$

Product of two numbers is >0 if both are >0 or both are <0. Since -38<0, x must be <0.

$$x<0$$