Solve 2x-1/3-x+6/4>x-6/16

$$\frac { 2 x - 1 } { 3 } - \frac { x + 6 } { 4 } > \frac { x - 6 } { 16 }$$

Solve for x

$$x>\frac{70}{17}$$

Solution Steps

Multiply both sides of the equation by 48, the least common multiple of 3,4,16. Since 48 is positive, the inequality direction remains the same.

$$16\left(2x-1\right)-12\left(x+6\right)>3\left(x-6\right)$$

Use the distributive property to multiply 16 by 2x-1.

$$32x-16-12\left(x+6\right)>3\left(x-6\right)$$

Use the distributive property to multiply -12 by x+6.

$$32x-16-12x-72>3\left(x-6\right)$$

Combine 32x and -12x to get 20x.

$$20x-16-72>3\left(x-6\right)$$

Subtract 72 from -16 to get -88.

$$20x-88>3\left(x-6\right)$$

Use the distributive property to multiply 3 by x-6.

$$20x-88>3x-18$$

Subtract 3x from both sides.

$$20x-88-3x>-18$$

Combine 20x and -3x to get 17x.

$$17x-88>-18$$

Add 88 to both sides.

$$17x>-18+88$$

Add -18 and 88 to get 70.

$$17x>70$$

Divide both sides by 17. Since 17 is positive, the inequality direction remains the same.

$$x>\frac{70}{17}$$