Solve x-2/6geqx-1/9+7/18

$$\frac { x - 2 } { 6 } \geq \frac { x - 1 } { 9 } + \frac { 7 } { 18 }$$

Solve for x

$$x\geq 11$$

Solution Steps

Multiply both sides of the equation by 18, the least common multiple of 6,9,18. Since 18 is positive, the inequality direction remains the same.

$$3\left(x-2\right)\geq 2\left(x-1\right)+7$$

Use the distributive property to multiply 3 by x-2.

$$3x-6\geq 2\left(x-1\right)+7$$

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

$$3x-6\geq 2x-2+7$$

Add -2 and 7 to get 5.

$$3x-6\geq 2x+5$$

Subtract 2x from both sides.

$$3x-6-2x\geq 5$$

Combine 3x and -2x to get x.

$$x-6\geq 5$$

Add 6 to both sides.

$$x\geq 5+6$$

Add 5 and 6 to get 11.

$$x\geq 11$$