Solve 2x-1/3>3x-4/7

$$\frac { 2 x - 1 } { 3 } > \frac { 3 x - 4 } { 7 }$$

Solve for x

$$x>-1$$

Solution Steps

Multiply both sides of the equation by 21, the least common multiple of 3,7. Since 21 is positive, the inequality direction remains the same.

$$7\left(2x-1\right)>3\left(3x-4\right)$$

Use the distributive property to multiply 7 by 2x-1.

$$14x-7>3\left(3x-4\right)$$

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

$$14x-7>9x-12$$

Subtract 9x from both sides.

$$14x-7-9x>-12$$

Combine 14x and -9x to get 5x.

$$5x-7>-12$$

Add 7 to both sides.

$$5x>-12+7$$

Add -12 and 7 to get -5.

$$5x>-5$$

Divide both sides by 5. Since 5 is positive, the inequality direction remains the same.

$$x>\frac{-5}{5}$$

Divide -5 by 5 to get -1.

$$x>-1$$