Solve 2-x-1/3<3x

$$2 - \frac { x - 1 } { 3 } < 3 x$$

Solve for x

$$x>\frac{7}{10}$$

Solution Steps

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

$$6-\left(x-1\right)<9x$$

To find the opposite of x-1, find the opposite of each term.

$$6-x-\left(-1\right)<9x$$

The opposite of -1 is 1.

$$6-x+1<9x$$

Add 6 and 1 to get 7.

$$7-x<9x$$

Subtract 9x from both sides.

$$7-x-9x<0$$

Combine -x and -9x to get -10x.

$$7-10x<0$$

Subtract 7 from both sides. Anything subtracted from zero gives its negation.

$$-10x<-7$$

Divide both sides by -10. Since -10 is negative, the inequality direction is changed.

$$x>\frac{-7}{-10}$$

Fraction \frac{-7}{-10} can be simplified to \frac{7}{10} by removing the negative sign from both the numerator and the denominator.

$$x>\frac{7}{10}$$