Solve x+7/2geq2x-1

$$\frac { x + 7 } { 2 } \geq 2 x - 1$$

Solve for x

$$x\leq 3$$

Solution Steps

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

$$x+7\geq 4x-2$$

Subtract 4x from both sides.

$$x+7-4x\geq -2$$

Combine x and -4x to get -3x.

$$-3x+7\geq -2$$

Subtract 7 from both sides.

$$-3x\geq -2-7$$

Subtract 7 from -2 to get -9.

$$-3x\geq -9$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

$$x\leq \frac{-9}{-3}$$

Divide -9 by -3 to get 3.

$$x\leq 3$$