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

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

Solve for x

$$x\geq -\frac{11}{2}$$

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.

$$3\left(2x+1\right)\geq 4\left(x+1\right)-12$$

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

$$6x+3\geq 4\left(x+1\right)-12$$

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

$$6x+3\geq 4x+4-12$$

Subtract 12 from 4 to get -8.

$$6x+3\geq 4x-8$$

Subtract 4x from both sides.

$$6x+3-4x\geq -8$$

Combine 6x and -4x to get 2x.

$$2x+3\geq -8$$

Subtract 3 from both sides.

$$2x\geq -8-3$$

Subtract 3 from -8 to get -11.

$$2x\geq -11$$

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

$$x\geq -\frac{11}{2}$$