Solve 5x-1/4-3x-13/10geq19/20x+21/20

$$\frac { 5 x - 1 } { 4 } - \frac { 3 x - 13 } { 10 } \geq \frac { 19 } { 20 } x + \frac { 21 } { 20 }$$

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

Multiply both sides of the equation by 20, the least common multiple of 4,10,20. Since 20 is positive, the inequality direction remains the same.

$$5\left(5x-1\right)-2\left(3x-13\right)\geq 19x+21$$

Use the distributive property to multiply 5 by 5x-1.

$$25x-5-2\left(3x-13\right)\geq 19x+21$$

Use the distributive property to multiply -2 by 3x-13.

$$25x-5-6x+26\geq 19x+21$$

Combine 25x and -6x to get 19x.

$$19x-5+26\geq 19x+21$$

Add -5 and 26 to get 21.

$$19x+21\geq 19x+21$$

Subtract 19x from both sides.

$$19x+21-19x\geq 21$$

Combine 19x and -19x to get 0.

$$21\geq 21$$

This is true for any x.

$$x\in \mathrm{R}$$