Solve x/8-x-1/4leqx-3

$$\frac { x } { 8 } - \frac { x - 1 } { 4 } \leq x - 3$$

Solve for x

$$x\geq \frac{26}{9}$$

Solution Steps

Multiply both sides of the equation by 8, the least common multiple of 8,4. Since 8 is positive, the inequality direction remains the same.

$$x-2\left(x-1\right)\leq 8x-24$$

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

$$x-2x+2\leq 8x-24$$

Combine x and -2x to get -x.

$$-x+2\leq 8x-24$$

Subtract 8x from both sides.

$$-x+2-8x\leq -24$$

Combine -x and -8x to get -9x.

$$-9x+2\leq -24$$

Subtract 2 from both sides.

$$-9x\leq -24-2$$

Subtract 2 from -24 to get -26.

$$-9x\leq -26$$

Divide both sides by -9. Since -9 is negative, the inequality direction is changed.

$$x\geq \frac{-26}{-9}$$

Fraction \frac{-26}{-9} can be simplified to \frac{26}{9} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{26}{9}$$