Solve x-1/2-x-3/4geq1

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

Solve for x

$$x\geq 3$$

Solution Steps

Multiply both sides of the equation by 4, the least common multiple of 2,4. Since 4 is positive, the inequality direction remains the same.

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

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

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

To find the opposite of x-3, find the opposite of each term.

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

The opposite of -3 is 3.

$$2x-2-x+3\geq 4$$

Combine 2x and -x to get x.

$$x-2+3\geq 4$$

Add -2 and 3 to get 1.

$$x+1\geq 4$$

Subtract 1 from both sides.

$$x\geq 4-1$$

Subtract 1 from 4 to get 3.

$$x\geq 3$$