Solve 4(x+1)geq3(x+3)-x

$$4(x+1) \geq 3(x+3)-x$$

Solve for x

$$x\geq \frac{5}{2}$$

Solution Steps

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

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

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

$$4x+4\geq 3x+9-x$$

Combine 3x and -x to get 2x.

$$4x+4\geq 2x+9$$

Subtract 2x from both sides.

$$4x+4-2x\geq 9$$

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

$$2x+4\geq 9$$

Subtract 4 from both sides.

$$2x\geq 9-4$$

Subtract 4 from 9 to get 5.

$$2x\geq 5$$

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

$$x\geq \frac{5}{2}$$