Solve (2x-1)/3geq3x-2/4-(2-x)/5

$$\frac { ( 2 x - 1 ) } { 3 } \geq \frac { 3 x - 2 } { 4 } - \frac { ( 2 - x ) } { 5 }$$

Solve for x

$$x\leq 2$$

Solution Steps

Multiply both sides of the equation by 60, the least common multiple of 3,4,5. Since 60 is positive, the inequality direction remains the same.

$$20\left(2x-1\right)\geq 15\left(3x-2\right)-12\left(2-x\right)$$

Use the distributive property to multiply 20 by 2x-1.

$$40x-20\geq 15\left(3x-2\right)-12\left(2-x\right)$$

Use the distributive property to multiply 15 by 3x-2.

$$40x-20\geq 45x-30-12\left(2-x\right)$$

Use the distributive property to multiply -12 by 2-x.

$$40x-20\geq 45x-30-24+12x$$

Subtract 24 from -30 to get -54.

$$40x-20\geq 45x-54+12x$$

Combine 45x and 12x to get 57x.

$$40x-20\geq 57x-54$$

Subtract 57x from both sides.

$$40x-20-57x\geq -54$$

Combine 40x and -57x to get -17x.

$$-17x-20\geq -54$$

Add 20 to both sides.

$$-17x\geq -54+20$$

Add -54 and 20 to get -34.

$$-17x\geq -34$$

Divide both sides by -17. Since -17 is negative, the inequality direction is changed.

$$x\leq \frac{-34}{-17}$$

Divide -34 by -17 to get 2.

$$x\leq 2$$