Solve 1-x-3/2geqx/2+5

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

Solve for x

$$x\leq -\frac{5}{2}$$

Solution Steps

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

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

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

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

The opposite of -3 is 3.

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

Add 2 and 3 to get 5.

$$5-x\geq x+10$$

Subtract x from both sides.

$$5-x-x\geq 10$$

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

$$5-2x\geq 10$$

Subtract 5 from both sides.

$$-2x\geq 10-5$$

Subtract 5 from 10 to get 5.

$$-2x\geq 5$$

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

$$x\leq -\frac{5}{2}$$