Solve 6>-2/3(7x-2)

$$6 > - \frac { 2 } { 3 } ( 7 x - 2 )$$

Solve for x

$$x>-1$$

Solution Steps

Multiply both sides by -\frac{3}{2}, the reciprocal of -\frac{2}{3}. Since -\frac{2}{3} is negative, the inequality direction is changed.

$$6\left(-\frac{3}{2}\right)<7x-2$$

Express 6\left(-\frac{3}{2}\right) as a single fraction.

$$\frac{6\left(-3\right)}{2}<7x-2$$

Multiply 6 and -3 to get -18.

$$\frac{-18}{2}<7x-2$$

Divide -18 by 2 to get -9.

$$-9<7x-2$$

Swap sides so that all variable terms are on the left hand side. This changes the sign direction.

$$7x-2>-9$$

Add 2 to both sides.

$$7x>-9+2$$

Add -9 and 2 to get -7.

$$7x>-7$$

Divide both sides by 7. Since 7 is positive, the inequality direction remains the same.

$$x>\frac{-7}{7}$$

Divide -7 by 7 to get -1.

$$x>-1$$