Solve x-16/6geqx-8/9+7/18

$$\frac { x - 16 } { 6 } \geq \frac { x - 8 } { 9 } + \frac { 7 } { 18 }$$

Solve for x

$$x\geq 39$$

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.

$$3\left(x-16\right)\geq 2\left(x-8\right)+7$$

Use the distributive property to multiply 3 by x-16.

$$3x-48\geq 2\left(x-8\right)+7$$

Use the distributive property to multiply 2 by x-8.

$$3x-48\geq 2x-16+7$$

Add -16 and 7 to get -9.

$$3x-48\geq 2x-9$$

Subtract 2x from both sides.

$$3x-48-2x\geq -9$$

Combine 3x and -2x to get x.

$$x-48\geq -9$$

Add 48 to both sides.

$$x\geq -9+48$$

Add -9 and 48 to get 39.

$$x\geq 39$$