Solve x-2x-1/5leq2x-3/4

$$x - \frac { 2 x - 1 } { 5 } \leq 2 x - \frac { 3 } { 4 }$$

Solve for x

$$x\geq \frac{19}{28}$$

Solution Steps

Multiply both sides of the equation by 20, the least common multiple of 5,4. Since 20 is positive, the inequality direction remains the same.

$$20x-4\left(2x-1\right)\leq 40x-15$$

Use the distributive property to multiply -4 by 2x-1.

$$20x-8x+4\leq 40x-15$$

Combine 20x and -8x to get 12x.

$$12x+4\leq 40x-15$$

Subtract 40x from both sides.

$$12x+4-40x\leq -15$$

Combine 12x and -40x to get -28x.

$$-28x+4\leq -15$$

Subtract 4 from both sides.

$$-28x\leq -15-4$$

Subtract 4 from -15 to get -19.

$$-28x\leq -19$$

Divide both sides by -28. Since -28 is negative, the inequality direction is changed.

$$x\geq \frac{-19}{-28}$$

Fraction \frac{-19}{-28} can be simplified to \frac{19}{28} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{19}{28}$$