Solve x-1/3leqx+1/9

$$\frac { x - 1 } { 3 } \leq \frac { x + 1 } { 9 }$$

Solve for x

$$x\leq 2$$

Solution Steps

Multiply both sides of the equation by 9, the least common multiple of 3,9. Since 9 is positive, the inequality direction remains the same.

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

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

$$3x-3\leq x+1$$

Subtract x from both sides.

$$3x-3-x\leq 1$$

Combine 3x and -x to get 2x.

$$2x-3\leq 1$$

Add 3 to both sides.

$$2x\leq 1+3$$

Add 1 and 3 to get 4.

$$2x\leq 4$$

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

$$x\leq \frac{4}{2}$$

Divide 4 by 2 to get 2.

$$x\leq 2$$