Solve 2-4x-1/9leq1/3+2x-5/6

$$2 - \frac { 4 x - 1 } { 9 } \leq \frac { 1 } { 3 } + \frac { 2 x - 5 } { 6 }$$

Solve for x

$$x\geq \frac{47}{14}$$

Solution Steps

Multiply both sides of the equation by 18, the least common multiple of 9,3,6. Since 18 is positive, the inequality direction remains the same.

$$36-2\left(4x-1\right)\leq 6+3\left(2x-5\right)$$

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

$$36-8x+2\leq 6+3\left(2x-5\right)$$

Add 36 and 2 to get 38.

$$38-8x\leq 6+3\left(2x-5\right)$$

Use the distributive property to multiply 3 by 2x-5.

$$38-8x\leq 6+6x-15$$

Subtract 15 from 6 to get -9.

$$38-8x\leq -9+6x$$

Subtract 6x from both sides.

$$38-8x-6x\leq -9$$

Combine -8x and -6x to get -14x.

$$38-14x\leq -9$$

Subtract 38 from both sides.

$$-14x\leq -9-38$$

Subtract 38 from -9 to get -47.

$$-14x\leq -47$$

Divide both sides by -14. Since -14 is negative, the inequality direction is changed.

$$x\geq \frac{-47}{-14}$$

Fraction \frac{-47}{-14} can be simplified to \frac{47}{14} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{47}{14}$$