Solve 3x-1/2+xleq2x+1/3-2

$$\frac{ 3x-1 }{ 2 } +x \leq \frac{ 2x+1 }{ 3 } -2$$

Solve for x

$$x\leq -\frac{7}{11}$$

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.

$$3\left(3x-1\right)+6x\leq 2\left(2x+1\right)-12$$

Use the distributive property to multiply 3 by 3x-1.

$$9x-3+6x\leq 2\left(2x+1\right)-12$$

Combine 9x and 6x to get 15x.

$$15x-3\leq 2\left(2x+1\right)-12$$

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

$$15x-3\leq 4x+2-12$$

Subtract 12 from 2 to get -10.

$$15x-3\leq 4x-10$$

Subtract 4x from both sides.

$$15x-3-4x\leq -10$$

Combine 15x and -4x to get 11x.

$$11x-3\leq -10$$

Add 3 to both sides.

$$11x\leq -10+3$$

Add -10 and 3 to get -7.

$$11x\leq -7$$

Divide both sides by 11. Since 11 is positive, the inequality direction remains the same.

$$x\leq -\frac{7}{11}$$