Solve 3x-7/6-4-5x/3>-1

$$\frac { 3 x - 7 } { 6 } - \frac { 4 - 5 x } { 3 } > - 1$$

Solve for x

$$x>\frac{9}{13}$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 6,3. Since 6 is positive, the inequality direction remains the same.

$$3x-7-2\left(4-5x\right)>-6$$

Use the distributive property to multiply -2 by 4-5x.

$$3x-7-8+10x>-6$$

Subtract 8 from -7 to get -15.

$$3x-15+10x>-6$$

Combine 3x and 10x to get 13x.

$$13x-15>-6$$

Add 15 to both sides.

$$13x>-6+15$$

Add -6 and 15 to get 9.

$$13x>9$$

Divide both sides by 13. Since 13 is positive, the inequality direction remains the same.

$$x>\frac{9}{13}$$