Solve 5x+1/5-2geqx-5/4

$$\frac{ 5x+1 }{ 5 } -2 \geq \frac{ x-5 }{ 4 }$$

Solve for x

$$x\geq \frac{11}{15}$$

Solution Steps

Multiply both sides of the equation by 20, the least common multiple of 5,4. Since 20 is positive, the inequality direction remains the same.

$$4\left(5x+1\right)-40\geq 5\left(x-5\right)$$

Use the distributive property to multiply 4 by 5x+1.

$$20x+4-40\geq 5\left(x-5\right)$$

Subtract 40 from 4 to get -36.

$$20x-36\geq 5\left(x-5\right)$$

Use the distributive property to multiply 5 by x-5.

$$20x-36\geq 5x-25$$

Subtract 5x from both sides.

$$20x-36-5x\geq -25$$

Combine 20x and -5x to get 15x.

$$15x-36\geq -25$$

Add 36 to both sides.

$$15x\geq -25+36$$

Add -25 and 36 to get 11.

$$15x\geq 11$$

Divide both sides by 15. Since 15 is positive, the inequality direction remains the same.

$$x\geq \frac{11}{15}$$