Solve 7-6x/2+10x<20x+1/3+2

$$\frac { 7 - 6 x } { 2 } + 10 x < \frac { 20 x + 1 } { 3 } + 2$$

Solve for x

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

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.

$$3\left(7-6x\right)+60x<2\left(20x+1\right)+12$$

Use the distributive property to multiply 3 by 7-6x.

$$21-18x+60x<2\left(20x+1\right)+12$$

Combine -18x and 60x to get 42x.

$$21+42x<2\left(20x+1\right)+12$$

Use the distributive property to multiply 2 by 20x+1.

$$21+42x<40x+2+12$$

Add 2 and 12 to get 14.

$$21+42x<40x+14$$

Subtract 40x from both sides.

$$21+42x-40x<14$$

Combine 42x and -40x to get 2x.

$$21+2x<14$$

Subtract 21 from both sides.

$$2x<14-21$$

Subtract 21 from 14 to get -7.

$$2x<-7$$

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

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