Solve 2x-1/4-5x+2/6>-1

$$\frac { 2 x - 1 } { 4 } - \frac { 5 x + 2 } { 6 } > - 1$$

Solve for x

$$x<\frac{5}{4}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,6. Since 12 is positive, the inequality direction remains the same.

$$3\left(2x-1\right)-2\left(5x+2\right)>-12$$

Use the distributive property to multiply 3 by 2x-1.

$$6x-3-2\left(5x+2\right)>-12$$

Use the distributive property to multiply -2 by 5x+2.

$$6x-3-10x-4>-12$$

Combine 6x and -10x to get -4x.

$$-4x-3-4>-12$$

Subtract 4 from -3 to get -7.

$$-4x-7>-12$$

Add 7 to both sides.

$$-4x>-12+7$$

Add -12 and 7 to get -5.

$$-4x>-5$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

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

Fraction \frac{-5}{-4} can be simplified to \frac{5}{4} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{5}{4}$$