Solve 9x-2/5-x/2geq2

$$\frac { 9 x - 2 } { 5 } - \frac { x } { 2 } \geq 2$$

Solve for x

$$x\geq \frac{24}{13}$$

Solution Steps

Multiply both sides of the equation by 10, the least common multiple of 5,2. Since 10 is positive, the inequality direction remains the same.

$$2\left(9x-2\right)-5x\geq 20$$

Use the distributive property to multiply 2 by 9x-2.

$$18x-4-5x\geq 20$$

Combine 18x and -5x to get 13x.

$$13x-4\geq 20$$

Add 4 to both sides.

$$13x\geq 20+4$$

Add 20 and 4 to get 24.

$$13x\geq 24$$

Divide both sides by 13. Since 13 is positive, the inequality direction remains the same.

$$x\geq \frac{24}{13}$$