Solve x/4-2x-1/5geqx

$$\frac { x } { 4 } - \frac { 2 x - 1 } { 5 } \geq x$$

Solve for x

$$x\leq \frac{4}{23}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 5 is 20. Multiply \frac{x}{4} times \frac{5}{5}. Multiply \frac{2x-1}{5} times \frac{4}{4}.

$$\frac{5x}{20}-\frac{4\left(2x-1\right)}{20}\geq x$$

Since \frac{5x}{20} and \frac{4\left(2x-1\right)}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5x-4\left(2x-1\right)}{20}\geq x$$

Do the multiplications in 5x-4\left(2x-1\right).

$$\frac{5x-8x+4}{20}\geq x$$

Combine like terms in 5x-8x+4.

$$\frac{-3x+4}{20}\geq x$$

Divide each term of -3x+4 by 20 to get -\frac{3}{20}x+\frac{1}{5}.

$$-\frac{3}{20}x+\frac{1}{5}\geq x$$

Subtract x from both sides.

$$-\frac{3}{20}x+\frac{1}{5}-x\geq 0$$

Combine -\frac{3}{20}x and -x to get -\frac{23}{20}x.

$$-\frac{23}{20}x+\frac{1}{5}\geq 0$$

Subtract \frac{1}{5} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{23}{20}x\geq -\frac{1}{5}$$

Multiply both sides by -\frac{20}{23}, the reciprocal of -\frac{23}{20}. Since -\frac{23}{20} is negative, the inequality direction is changed.

$$x\leq -\frac{1}{5}\left(-\frac{20}{23}\right)$$

Multiply -\frac{1}{5} times -\frac{20}{23} by multiplying numerator times numerator and denominator times denominator.

$$x\leq \frac{-\left(-20\right)}{5\times 23}$$

Do the multiplications in the fraction \frac{-\left(-20\right)}{5\times 23}.

$$x\leq \frac{20}{115}$$

Reduce the fraction \frac{20}{115} to lowest terms by extracting and canceling out 5.

$$x\leq \frac{4}{23}$$