Solve x-5/4leqx

$$\frac { x - 5 } { 4 } \leq x$$

Solve for x

$$x\geq -\frac{5}{3}$$

Solution Steps

Divide each term of x-5 by 4 to get \frac{1}{4}x-\frac{5}{4}.

$$\frac{1}{4}x-\frac{5}{4}\leq x$$

Subtract x from both sides.

$$\frac{1}{4}x-\frac{5}{4}-x\leq 0$$

Combine \frac{1}{4}x and -x to get -\frac{3}{4}x.

$$-\frac{3}{4}x-\frac{5}{4}\leq 0$$

Add \frac{5}{4} to both sides. Anything plus zero gives itself.

$$-\frac{3}{4}x\leq \frac{5}{4}$$

Multiply both sides by -\frac{4}{3}, the reciprocal of -\frac{3}{4}. Since -\frac{3}{4} is negative, the inequality direction is changed.

$$x\geq \frac{5}{4}\left(-\frac{4}{3}\right)$$

Multiply \frac{5}{4} times -\frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$x\geq \frac{5\left(-4\right)}{4\times 3}$$

Do the multiplications in the fraction \frac{5\left(-4\right)}{4\times 3}.

$$x\geq \frac{-20}{12}$$

Reduce the fraction \frac{-20}{12} to lowest terms by extracting and canceling out 4.

$$x\geq -\frac{5}{3}$$