Solve x/3-2x-x/6leq3left(x+1right)

$$\frac{ x }{ 3 } - \frac{ 2x-x }{ 6 } \leq 3 \left( x+1 \right)$$

Solve for x

$$x\geq -\frac{18}{17}$$

Solution Steps

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

$$2x-\left(2x-x\right)\leq 18\left(x+1\right)$$

Combine 2x and -x to get x.

$$2x-x\leq 18\left(x+1\right)$$

Use the distributive property to multiply 18 by x+1.

$$2x-x\leq 18x+18$$

Subtract 18x from both sides.

$$2x-x-18x\leq 18$$

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

$$-16x-x\leq 18$$

Combine -16x and -x to get -17x.

$$-17x\leq 18$$

Divide both sides by -17. Since -17 is negative, the inequality direction is changed.

$$x\geq -\frac{18}{17}$$