Solve 3x/10+1geq1/5-x/10

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

Solve for x

$$x\geq -2$$

Solution Steps

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

$$3x+10\geq 2-x$$

Add x to both sides.

$$3x+10+x\geq 2$$

Combine 3x and x to get 4x.

$$4x+10\geq 2$$

Subtract 10 from both sides.

$$4x\geq 2-10$$

Subtract 10 from 2 to get -8.

$$4x\geq -8$$

Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.

$$x\geq \frac{-8}{4}$$

Divide -8 by 4 to get -2.

$$x\geq -2$$