Solve 1-5x/6-2/5leq3-x/4

$$\frac { 1 - 5 x } { 6 } - \frac { 2 } { 5 } \leq \frac { 3 - x } { 4 }$$

Solve for x

$$x\geq -\frac{59}{35}$$

Solution Steps

Multiply both sides of the equation by 60, the least common multiple of 6,5,4. Since 60 is positive, the inequality direction remains the same.

$$10\left(1-5x\right)-24\leq 15\left(3-x\right)$$

Use the distributive property to multiply 10 by 1-5x.

$$10-50x-24\leq 15\left(3-x\right)$$

Subtract 24 from 10 to get -14.

$$-14-50x\leq 15\left(3-x\right)$$

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

$$-14-50x\leq 45-15x$$

Add 15x to both sides.

$$-14-50x+15x\leq 45$$

Combine -50x and 15x to get -35x.

$$-14-35x\leq 45$$

Add 14 to both sides.

$$-35x\leq 45+14$$

Add 45 and 14 to get 59.

$$-35x\leq 59$$

Divide both sides by -35. Since -35 is negative, the inequality direction is changed.

$$x\geq -\frac{59}{35}$$