Solve x-27-1/3geq2+x/2-1

$$x - \frac { 27 - 1 } { 3 } \geq \frac { 2 + x } { 2 } - 1$$

Solve for x

$$x\geq \frac{52}{3}$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2. Since 6 is positive, the inequality direction remains the same.

$$6x-2\left(27-1\right)\geq 3\left(2+x\right)-6$$

Subtract 1 from 27 to get 26.

$$6x-2\times 26\geq 3\left(2+x\right)-6$$

Multiply -2 and 26 to get -52.

$$6x-52\geq 3\left(2+x\right)-6$$

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

$$6x-52\geq 6+3x-6$$

Subtract 6 from 6 to get 0.

$$6x-52\geq 3x$$

Subtract 3x from both sides.

$$6x-52-3x\geq 0$$

Combine 6x and -3x to get 3x.

$$3x-52\geq 0$$

Add 52 to both sides. Anything plus zero gives itself.

$$3x\geq 52$$

Divide both sides by 3. Since 3 is positive, the inequality direction remains the same.

$$x\geq \frac{52}{3}$$