Solve 3x+1/4-1/3leq2/15(3x+2)+4(1-x)/3

$$\frac { 3 x + 1 } { 4 } - \frac { 1 } { 3 } \leq \frac { 2 } { 15 } ( 3 x + 2 ) + \frac { 4 ( 1 - x ) } { 3 }$$

Solve for x

$$x\leq 1$$

Solution Steps

Multiply both sides of the equation by 60, the least common multiple of 4,3,15. Since 60 is positive, the inequality direction remains the same.

$$15\left(3x+1\right)-20\leq 8\left(3x+2\right)+20\times 4\left(1-x\right)$$

Use the distributive property to multiply 15 by 3x+1.

$$45x+15-20\leq 8\left(3x+2\right)+20\times 4\left(1-x\right)$$

Subtract 20 from 15 to get -5.

$$45x-5\leq 8\left(3x+2\right)+20\times 4\left(1-x\right)$$

Use the distributive property to multiply 8 by 3x+2.

$$45x-5\leq 24x+16+20\times 4\left(1-x\right)$$

Multiply 20 and 4 to get 80.

$$45x-5\leq 24x+16+80\left(1-x\right)$$

Use the distributive property to multiply 80 by 1-x.

$$45x-5\leq 24x+16+80-80x$$

Add 16 and 80 to get 96.

$$45x-5\leq 24x+96-80x$$

Combine 24x and -80x to get -56x.

$$45x-5\leq -56x+96$$

Add 56x to both sides.

$$45x-5+56x\leq 96$$

Combine 45x and 56x to get 101x.

$$101x-5\leq 96$$

Add 5 to both sides.

$$101x\leq 96+5$$

Add 96 and 5 to get 101.

$$101x\leq 101$$

Divide both sides by 101. Since 101 is positive, the inequality direction remains the same.

$$x\leq \frac{101}{101}$$

Divide 101 by 101 to get 1.

$$x\leq 1$$