Solve x-5/2-1geq3(x+2)

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

Solve for x

$$x\leq -\frac{19}{5}$$

Solution Steps

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

$$x-5-2\geq 6\left(x+2\right)$$

Subtract 2 from -5 to get -7.

$$x-7\geq 6\left(x+2\right)$$

Use the distributive property to multiply 6 by x+2.

$$x-7\geq 6x+12$$

Subtract 6x from both sides.

$$x-7-6x\geq 12$$

Combine x and -6x to get -5x.

$$-5x-7\geq 12$$

Add 7 to both sides.

$$-5x\geq 12+7$$

Add 12 and 7 to get 19.

$$-5x\geq 19$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$x\leq -\frac{19}{5}$$