Solve 2x-8x+1geqx+3/2

$$2 x - 8 x + 1 \geq \frac { x + 3 } { 2 }$$

Solve for x

$$x\leq -\frac{1}{13}$$

Solution Steps

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

$$4x-16x+2\geq x+3$$

Combine 4x and -16x to get -12x.

$$-12x+2\geq x+3$$

Subtract x from both sides.

$$-12x+2-x\geq 3$$

Combine -12x and -x to get -13x.

$$-13x+2\geq 3$$

Subtract 2 from both sides.

$$-13x\geq 3-2$$

Subtract 2 from 3 to get 1.

$$-13x\geq 1$$

Divide both sides by -13. Since -13 is negative, the inequality direction is changed.

$$x\leq -\frac{1}{13}$$