Solve 1/2(2-7x)<x/3-1(3x+2)

$$\frac{ 1 }{ 2 } (2-7x) < \frac{ x }{ 3 } -1(3x+2)$$

Solve for x

$$x>\frac{18}{5}$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 2,3. Since 6 is positive, the inequality direction remains the same.

$$3\left(2-7x\right)<2x-6\left(3x+2\right)$$

Use the distributive property to multiply 3 by 2-7x.

$$6-21x<2x-6\left(3x+2\right)$$

Use the distributive property to multiply -6 by 3x+2.

$$6-21x<2x-18x-12$$

Combine 2x and -18x to get -16x.

$$6-21x<-16x-12$$

Add 16x to both sides.

$$6-21x+16x<-12$$

Combine -21x and 16x to get -5x.

$$6-5x<-12$$

Subtract 6 from both sides.

$$-5x<-12-6$$

Subtract 6 from -12 to get -18.

$$-5x<-18$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$x>\frac{-18}{-5}$$

Fraction \frac{-18}{-5} can be simplified to \frac{18}{5} by removing the negative sign from both the numerator and the denominator.

$$x>\frac{18}{5}$$