Solve x+2/2-4x-1/6geq1

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

Solve for x

$$x\leq 1$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 2,6. Since 6 is positive, the inequality direction remains the same.

$$3\left(x+2\right)-\left(4x-1\right)\geq 6$$

Use the distributive property to multiply 3 by x+2.

$$3x+6-\left(4x-1\right)\geq 6$$

To find the opposite of 4x-1, find the opposite of each term.

$$3x+6-4x-\left(-1\right)\geq 6$$

The opposite of -1 is 1.

$$3x+6-4x+1\geq 6$$

Combine 3x and -4x to get -x.

$$-x+6+1\geq 6$$

Add 6 and 1 to get 7.

$$-x+7\geq 6$$

Subtract 7 from both sides.

$$-x\geq 6-7$$

Subtract 7 from 6 to get -1.

$$-x\geq -1$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

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

Divide -1 by -1 to get 1.

$$x\leq 1$$