Solve x-1/72+1geqx

$$\frac { x - 1 } { 72 } + 1 \geq x$$

Solve for x

$$x\leq 1$$

Solution Steps

Divide each term of x-1 by 72 to get \frac{1}{72}x-\frac{1}{72}.

$$\frac{1}{72}x-\frac{1}{72}+1\geq x$$

Convert 1 to fraction \frac{72}{72}.

$$\frac{1}{72}x-\frac{1}{72}+\frac{72}{72}\geq x$$

Since -\frac{1}{72} and \frac{72}{72} have the same denominator, add them by adding their numerators.

$$\frac{1}{72}x+\frac{-1+72}{72}\geq x$$

Add -1 and 72 to get 71.

$$\frac{1}{72}x+\frac{71}{72}\geq x$$

Subtract x from both sides.

$$\frac{1}{72}x+\frac{71}{72}-x\geq 0$$

Combine \frac{1}{72}x and -x to get -\frac{71}{72}x.

$$-\frac{71}{72}x+\frac{71}{72}\geq 0$$

Subtract \frac{71}{72} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{71}{72}x\geq -\frac{71}{72}$$

Multiply both sides by -\frac{72}{71}, the reciprocal of -\frac{71}{72}. Since -\frac{71}{72} is negative, the inequality direction is changed.

$$x\leq -\frac{71}{72}\left(-\frac{72}{71}\right)$$

Multiply -\frac{71}{72} times -\frac{72}{71} by multiplying numerator times numerator and denominator times denominator.

$$x\leq \frac{-71\left(-72\right)}{72\times 71}$$

Do the multiplications in the fraction \frac{-71\left(-72\right)}{72\times 71}.

$$x\leq \frac{5112}{5112}$$

Divide 5112 by 5112 to get 1.

$$x\leq 1$$