Solve -x/5+1leq3x/10-2

$$\frac { - x } { 5 } + 1 \leq \frac { 3 x } { 10 } - 2$$

Solve for x

$$x\geq 6$$

Solution Steps

Multiply both sides of the equation by 10, the least common multiple of 5,10. Since 10 is positive, the inequality direction remains the same.

$$2\left(-x\right)+10\leq 3x-20$$

Subtract 3x from both sides.

$$2\left(-x\right)+10-3x\leq -20$$

Subtract 10 from both sides.

$$2\left(-x\right)-3x\leq -20-10$$

Subtract 10 from -20 to get -30.

$$2\left(-x\right)-3x\leq -30$$

Multiply 2 and -1 to get -2.

$$-2x-3x\leq -30$$

Combine -2x and -3x to get -5x.

$$-5x\leq -30$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$x\geq \frac{-30}{-5}$$

Divide -30 by -5 to get 6.

$$x\geq 6$$