Solve 2-x/4geq1-x/3

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

Solve for x

$$x\geq -2$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,3. Since 12 is positive, the inequality direction remains the same.

$$3\left(2-x\right)\geq 4\left(1-x\right)$$

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

$$6-3x\geq 4\left(1-x\right)$$

Use the distributive property to multiply 4 by 1-x.

$$6-3x\geq 4-4x$$

Add 4x to both sides.

$$6-3x+4x\geq 4$$

Combine -3x and 4x to get x.

$$6+x\geq 4$$

Subtract 6 from both sides.

$$x\geq 4-6$$

Subtract 6 from 4 to get -2.

$$x\geq -2$$