Solve 1/2(8x+1)geq3x+5/2

$$\frac{ 1 }{ 2 } (8x+1) \geq 3x+ \frac{ 5 }{ 2 }$$

Solve for x

$$x\geq 2$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by 8x+1.

$$\frac{1}{2}\times 8x+\frac{1}{2}\geq 3x+\frac{5}{2}$$

Multiply \frac{1}{2} and 8 to get \frac{8}{2}.

$$\frac{8}{2}x+\frac{1}{2}\geq 3x+\frac{5}{2}$$

Divide 8 by 2 to get 4.

$$4x+\frac{1}{2}\geq 3x+\frac{5}{2}$$

Subtract 3x from both sides.

$$4x+\frac{1}{2}-3x\geq \frac{5}{2}$$

Combine 4x and -3x to get x.

$$x+\frac{1}{2}\geq \frac{5}{2}$$

Subtract \frac{1}{2} from both sides.

$$x\geq \frac{5}{2}-\frac{1}{2}$$

Since \frac{5}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$x\geq \frac{5-1}{2}$$

Subtract 1 from 5 to get 4.

$$x\geq \frac{4}{2}$$

Divide 4 by 2 to get 2.

$$x\geq 2$$