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

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

Solve for x

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

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.

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

To find the opposite of 2x-1, find the opposite of each term.

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

The opposite of -1 is 1.

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

Combine 2x and -2x to get 0.

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

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

$$1\leq 18x+18$$

Swap sides so that all variable terms are on the left hand side. This changes the sign direction.

$$18x+18\geq 1$$

Subtract 18 from both sides.

$$18x\geq 1-18$$

Subtract 18 from 1 to get -17.

$$18x\geq -17$$

Divide both sides by 18. Since 18 is positive, the inequality direction remains the same.

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