Solve x+1/4geq-2-x-1/3

$$\frac { x + 1 } { 4 } \geq - 2 - \frac { x - 1 } { 3 }$$

Solve for x

$$x\geq -\frac{23}{7}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,3. Since 12 is positive, the inequality direction remains the same.

$$3\left(x+1\right)\geq -24-4\left(x-1\right)$$

Use the distributive property to multiply 3 by x+1.

$$3x+3\geq -24-4\left(x-1\right)$$

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

$$3x+3\geq -24-4x+4$$

Add -24 and 4 to get -20.

$$3x+3\geq -20-4x$$

Add 4x to both sides.

$$3x+3+4x\geq -20$$

Combine 3x and 4x to get 7x.

$$7x+3\geq -20$$

Subtract 3 from both sides.

$$7x\geq -20-3$$

Subtract 3 from -20 to get -23.

$$7x\geq -23$$

Divide both sides by 7. Since 7 is positive, the inequality direction remains the same.

$$x\geq -\frac{23}{7}$$