Solve 5x+3x-2/5-74/5geq2x

$$5 x + \frac { 3 x - 2 } { 5 } - \frac { 74 } { 5 } \geq 2 x$$

Solve for x

$$x\geq \frac{38}{9}$$

Solution Steps

Multiply both sides of the equation by 5. Since 5 is positive, the inequality direction remains the same.

$$25x+3x-2-74\geq 10x$$

Combine 25x and 3x to get 28x.

$$28x-2-74\geq 10x$$

Subtract 74 from -2 to get -76.

$$28x-76\geq 10x$$

Subtract 10x from both sides.

$$28x-76-10x\geq 0$$

Combine 28x and -10x to get 18x.

$$18x-76\geq 0$$

Add 76 to both sides. Anything plus zero gives itself.

$$18x\geq 76$$

Divide both sides by 18. Since 18 is positive, the inequality direction remains the same.

$$x\geq \frac{76}{18}$$

Reduce the fraction \frac{76}{18} to lowest terms by extracting and canceling out 2.

$$x\geq \frac{38}{9}$$