Solve 7-x/4>1-3x/6

$$\frac{ 7-x }{ 4 } > \frac{ 1-3x }{ 6 }$$

Solve for x

$$x>-\frac{19}{3}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,6. Since 12 is positive, the inequality direction remains the same.

$$3\left(7-x\right)>2\left(1-3x\right)$$

Use the distributive property to multiply 3 by 7-x.

$$21-3x>2\left(1-3x\right)$$

Use the distributive property to multiply 2 by 1-3x.

$$21-3x>2-6x$$

Add 6x to both sides.

$$21-3x+6x>2$$

Combine -3x and 6x to get 3x.

$$21+3x>2$$

Subtract 21 from both sides.

$$3x>2-21$$

Subtract 21 from 2 to get -19.

$$3x>-19$$

Divide both sides by 3. Since 3 is positive, the inequality direction remains the same.

$$x>-\frac{19}{3}$$